Change search
Refine search result
1 - 33 of 33
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Andersson, Lennart
    et al.
    Luleå tekniska universitet.
    Grennberg, Anders
    Hedberg, Torbjörn
    Luleå tekniska universitet.
    Näslund, Reinhold
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    von Sydow, Björn
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Linjär algebra med geometri1999Book (Other (popular science, discussion, etc.))
  • 2.
    Berglund, Tomas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Brodnik, Andrej
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Jonsson, Håkan
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Mrozek, Kent
    Staffansson, Mats
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Minimum curvature variation B-splines: validation of a path-planning model2004Report (Other academic)
  • 3.
    Berglund, Tomas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Brodnik, Andrej
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science. University of Primorska, Slovenia. .
    Jonsson, Håkan
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Staffansson, Mats
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles2010In: IEEE Transactions on Automation Science and Engineering, ISSN 1545-5955, E-ISSN 1558-3783, Vol. 7, no 1, p. 167-172Article in journal (Refereed)
    Abstract [en]

    We study the problem of automatic generation of smooth and obstacle-avoiding planar paths for efficient guidance of autonomous mining vehicles. Fast traversal of a path is of special interest. We consider four-wheel four-gear articulated vehicles and assume that we have an a priori knowledge of the mine wall environment in the form of polygonal chains. Computing quartic uniform B-spline curves, minimizing curvature variation, staying at least at a proposed safety margin distance from the mine walls, we plan high speed paths.

  • 4.
    Berglund, Tomas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Erikson, Ulf
    Luleå tekniska universitet.
    Jonsson, Håkan
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Mrozek, Kent
    Navigator AB.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Automatic generation of smooth paths bounded by polygonal chains2001In: CIMCA 2001: 2001 international conference on computational intelligence for modelling, control & automation : 9-11 July 2001, Las Vegas, Nevada, USA : proceedings / [ed] M. Mohammadian, CIMCA , 2001, p. 528-535Conference paper (Refereed)
  • 5. Berglund, Tomas
    et al.
    Jonsson, Håkan
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    An obstacle-avoiding minimum variation B-spline problem2003In: Proceedings: 2003 International Conference on Geometric Modeling and Graphics, GMAG 2003 ; 16 - 18 July 2003, London, England, Los Alamitos, Calif: IEEE Communications Society, 2003, p. 156-161Conference paper (Refereed)
    Abstract [en]

    We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

  • 6.
    Berglund, Tomas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Jonsson, Håkan
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    The problem of computing an obstacle-avoiding minimum variation B-spline2003Report (Other academic)
    Abstract [en]

    We study the problem of computing a planar curve restricted to lie between two given polygonal chains such that the integral of the square of arc- length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

  • 7.
    Berglund, Tomas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Strömberg, Thomas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Jonsson, Håkan
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Epi-convergence of minimum curvature variation B-splines2003Report (Other academic)
    Abstract [en]

    We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.

  • 8.
    Berglund, Tomas
    et al.
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Synnergren, Per
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Estimation of curl in paper: an industrial application combining shape measurement and least squares modeling2000In: Proceedings / International Conference on Trends in Optical Nondestructive Testing: Lugano, Switzerland, May 3-6, 2000 / [ed] Pramod K. Rastogi; D. Inaudi, Lugano: Ecole Polytechnique Fédérale de Lausanne , 2000, p. 23-33Conference paper (Refereed)
    Abstract [en]

    If a sheet of paper is subjected to humidity changes and have structural variations through its thickness such as gradients of fibre orientation, density and filler content, the sheet will curl and hence assume a cylindrical shape. Curl is a quality problem that makes the paper less suitable for printing. We propose a method to measure curl that can be used for automated analysis of the paper quality. The shape of the curled paper is measured from the perspective difference in a stereoscopic camera system, which is viewing an irregular pattern that is projected onto the specimen. The perspective difference is calculated by a correlation algorithm, a technique often referred to as digital speckle photography. The most interesting quality parameters are the magnitude of curl, which is defined as the inverse of the radius of curvature and also the orientation of the curled paper. These parameters are estimated by performing a least squares fit of a cylindrical shape to the three-dimension...

  • 9.
    Bergström, Per
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Edlund, Ove
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR2012In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, no 3, p. 571-588Article in journal (Refereed)
    Abstract [en]

    We consider a subproblem in parameter estimation using the Gauss-Newton algorithm with regularization for NURBS curve fitting. The NURBS curve is fitted to a set of data points in least-squares sense, where the sum of squared orthogonal distances is minimized. Control-points and weights are estimated. The knot-vector and the degree of the NURBS curve are kept constant. In the Gauss-Newton algorithm, a search direction is obtained from a linear overdetermined system with a Jacobian and a residual vector. Because of the properties of our problem, the Jacobian has a particular sparse structure which is suitable for performing a splitting of variables. We are handling the computational problems and report the obtained accuracy using different methods, and the elapsed real computational time. The splitting of variables is a two times faster method than using plain normal equations.

  • 10.
    Bergström, Per
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Edlund, Ove
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    Repeated surface registration for on-line use2011In: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 54, no 5-8, p. 677-689Article in journal (Refereed)
    Abstract [en]

    We consider the problem of matching sets of 3D points from a measured surface to the surface of a corresponding computer-aided design (CAD) object. The problem arises in the production line where the shape of the produced items is to be compared on-line with its pre-described shape. The involved registration problem is solved using the iterative closest point (ICP) method. In order to make it suitable for on-line use, i.e., make it fast, we pre-process the surface representation of the CAD object. A data structure for this purpose is proposed and named Distance Varying Grid tree. It is based on a regular grid that encloses points sampled from the CAD surfaces. Additional finer grids are added to the vertices in the grid that are close to the sampled points. The structure is efficient since it utilizes that the sampled points are distributed on surfaces, and it provides fast identification of the sampled point that is closest to a measured point. A local linear approximation of the surface is used for improving the accuracy. Experiments are done on items produced for the body of a car. The experiments show that it is possible to reach good accuracy in the registration and decreasing the computational time by a factor 700 compared with using the common kd-tree structure.

  • 11.
    Bergström, Per
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Fitting NURBS using separable least squares techniques2012In: International Journal of Mathematical Modelling and Numerical Optimisation, ISSN 2040-3607, E-ISSN 2040-3615, Vol. 3, no 4, p. 319-334Article in journal (Refereed)
    Abstract [en]

    We consider the problem of fitting a non-uniform rational B-spline (NURBS) curve to a set of data points by determining the control points and the weights using techniques aimed for solving separable least squares problems. The main technique under consideration is the variable projection method which utilises that the NURBS model depends linearly on its control points but non-linearly on the weights. The variable projection method can be used with the Gauss-Newton algorithm but also with Newton's algorithm. We investigate the efficiency of the different algorithms when fitting NURBS and observe that the variable projection methods do not perform as well as reported for its use on, e.g., exponential fitting problems.

  • 12.
    Eriksson, J.
    et al.
    Department of Computing Science, Umeå University.
    Wedin, P. A.
    Department of Computing Science, Umeå University.
    Gulliksson, M. E.
    Department of Engineering, Physics, and Mathematics, Mid-Sweden University, Sundsvall.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Regularization methods for uniformly rank-deficient nonlinear least-squares problems2005In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 127, no 1, p. 1-26Article in journal (Refereed)
    Abstract [en]

    In solving the nonlinear least-squares problem of minimizing ||f(x)||22, difficulties arise with standard approaches, such as the Levenberg-Marquardt approach, when the Jacobian of f is rank-deficient or very ill-conditioned at the solution. To handle this difficulty, we study a special class of least-squares problems that are uniformly rank-deficient, i.e., the Jacobian of f has the same deficient rank in the neighborhood of a solution. For such problems, the solution is not locally unique. We present two solution tecniques: (i) finding a minimum-norm solution to the basic problem, (ii) using a Tikhonov regularization. Optimality conditions and algorithms are given for both of these strategies. Asymptotical convergence properties of the algorithms are derived and confirmed by numerical experiments. Extensions of the presented ideas make it possible to solve more general nonlinear least-squares problems in which the Jacobian of f at the solution is rank-deficient or ill-conditioned.

  • 13.
    Gulliksson, M.
    et al.
    Department of Physics and Mathematics, Mid Sweden University.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Watson, G. A.
    Department of Mathematics, University of Dundee.
    Implicit surface fitting using directional constraints2001In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 41, no 1, p. 308-321Article in journal (Refereed)
    Abstract [en]

    A commonly used technique for fitting curves and surfaces to measured data is that known as orthogonal distance regression, where the sum of squares of orthogonal distances from the data points to the surface is minimized. An alternative has recently been proposed for curves and surfaces which are parametrically defined, which minimizes the sum of squares in given directions which depend on the measuring process. In addition to taking account of that process, it is claimed that this technique has the advantage of complying with traditional fixed-regressor assumptions, enabling standard inference theory to apply. Here we consider extending this idea to curves and surfaces where the only assumption made is that there is an implicit formulation. Numerical results are given to illustrate the algorithmic performance.

  • 14. Gulliksson, Mårten
    et al.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Surface Fitting and Parameter Estimation with Nonlinear Least Squares1995In: Optimization Methods and Software, ISSN 1055-6788, E-ISSN 1029-4937, Vol. 5, p. 247-269Article in journal (Refereed)
    Abstract [en]

    Algorithms for fitting a surface, explicitly or implicitly defined, to some measured points are developed, analyzed and tested. The problem class treated, includes orthogonal regression and errors-in-variables. Methods using only first order derivatives as well as second order methods are developed and the rich inherent structure of the problem is fully utilized. The main features of the algorithms, that distinguish them from earlier works, are that arbitrary nonnegative weights can be handled and that infinite weights can be used to define nonlinear equality constraints. Moreover, by using a special merit function, global convergence can be proved for the first order methods under some nondegeneracy assumptions. The local convergence for the first order algorithms is linear for nonzero residual problems and quadratic otherwise. The local convergence for the second order methods is quadratic. A mixed algorithm where only a part of the second derivatives are included is also developed and tested.

  • 15.
    Gulliksson, Mårten
    et al.
    Institution of Information Processing, University of Umeå.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedin, Per-Åke
    Institution of Information Processing, University of Umeå.
    Algorithms for constrained and weighted nonlinear least squares1997In: SIAM Journal on Optimization, ISSN 1052-6234, E-ISSN 1095-7189, Vol. 7, no 1, p. 208-224Article in journal (Refereed)
    Abstract [en]

    The authors consider constrained and weighted nonlinear least squares problems in which weights can be arbitrarily large. Methods of Newton type are used for solving such problems: a Gauss-Newton method, a second-order generalized Newton-Raphson method, and an efficient hybrid approach consisting of both methods are suggested. Local convergence and global convergence under certain assumptions are proved for the Gauss-Newton method. Results of computational testing of the algorithm suggested are presented and an open problem is formulated at the end of the paper.

  • 16.
    Kärrholm, J.
    et al.
    Department of Orthopaedics, Sahlgren Hospital.
    Jonsson, H.
    Department of Orthopaedics, Northern University Hospital.
    Nilsson, K.G.
    Department of Orthopaedics, Northern University Hospital.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Kinematics of successful knee prostheses during weight-bearing: three-dimensional movements and positions of screw axes in the Tricon-M and Miller-Galante designs1994In: Knee Surgery, Sports Traumatology, Arthroscopy, ISSN 0942-2056, E-ISSN 1433-7347, Vol. 2, no 1, p. 50-59Article in journal (Refereed)
    Abstract [en]

    Using roentgen stereophotogrammetric analysis we recorded the three-dimensional movements in six knees with implanted Tricon-M prostheses and ten knees with Miller-Galante prostheses as the patients ascended a platform. Fourteen patients with normal knees were used as controls. The two prosthetic designs displayed decreased internal tibial rotation and the Tricon-M increased valgus rotation. A central point on the tibial articular surface had a more lateral position in the Tricon-M design and a more distal one in the Miller-Galante design compared to normal knees. Increased posterior displacement with increasing flexion was observed in both designs. When the normal knees were extended at full weightbearing the helical axes mainly shifted inclination in the frontal plane. In the prosthetic knees there was a tendency to anterior-posterior displacement of the axes as extension proceeded, especially in the Miller-Galante design. Translations along the helical axes were larger than normal in the Miller-Galante and smaller in the Tricon-M knees, reflecting differences in constraint of the two designs.

  • 17. Nyström, L.
    et al.
    Söderkvist, Inge
    KINERR Program documentation1989Report (Other academic)
  • 18. Nyström, L.
    et al.
    Söderkvist, Inge
    KINERR User's Guide1989Report (Other academic)
  • 19. Nyström, L.
    et al.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedin, P.-Å.
    A note on some identification problems arising in Roentgen stereo photogrammetric analysis1994In: Journal of Biomechanics, ISSN 0021-9290, E-ISSN 1873-2380, Vol. 27, p. 1291-1294Article in journal (Refereed)
    Abstract [en]

    When studying skeleton movements by using implanted landmarks and Roentgen Stereo Photogrammetric Analysis (RSA), some identification problems arise. One is to put the same label on a landmark at different examinations, another is to use the correct pairs of landmark images in order to compute a correct 3-D position of each landmark. We will present some methods that can be used as a support for solving these problems. We will also show how it is possible to detect and exclude landmarks that are loose and landmarks that have large measurement errors in their positions.

  • 20.
    Osborne, M. R.
    et al.
    School of Mathematical Sciences, Australian National University.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    V-invariant methods, generalised least squares problems, and the Kalman filter2004In: ANZIAM journal (Print), ISSN 1446-1811, E-ISSN 1446-8735, Vol. 45, no Part C, p. 232-247Article in journal (Refereed)
    Abstract [en]

    V-invariant methods for the generalised least squares problem extend the techniques based on orthogonal factorization for ordinary least squares to problems with multiscaled, even singular covariances. These methods are summarised briefly here, and the ability to handle multiple scales indicated. An application to a class of Kalman filter problems derived from generalised smoothing splines is considered. Evidence of severe illconditioning of the covariance matrices is demonstrated in several examples. This suggests that this is an appropriate application for the V-invariant techniques.

  • 21. Synnergren, Per
    et al.
    Berglund, Tomas
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Estimation of curl in paper using a combination of shape measurement and least-squares modelling2001In: Optics and lasers in engineering, ISSN 0143-8166, E-ISSN 1873-0302, Vol. 35, no 2, p. 105-120Article in journal (Refereed)
    Abstract [en]

    Curl is a quality problem that makes paper less suitable for printing. A paper sheet that has structural variations in its thickness such as gradients of fibre orientation, density and filler content, will curl and hence assume a cylindrical shape when its humidity content is changed. We propose a method to measure curl that can be used for automated analysis of the paper quality. The shape of the curled paper is measured using a stereoscopic camera system, which is capable of viewing a random pattern that is projected onto the specimen. The shape of the object is found by calculating the perspective difference in the camera set-up using digital image correlation. The quality parameters that are searched for are the magnitude of curl, which is defined as the inverse of the radius of curvature and the orientation of the curled paper. These parameters are estimated by performing a least-squares fit of a cylindrical shape to the three-dimensional measurement

  • 22.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    An algorithm for Kalman filtering and smoothing with diagonal input covariance matrices1996In: Computational techniques and applications, CTAC95: proceedings of the Seventh Biennial Conference held at Swinburne University of Technology, Melbourne, July 3--5, 1995 / [ed] Robert L. May; Alan K. Easton, World Scientific Publishing Co Pte Ltd , 1996, p. 709-716Conference paper (Refereed)
    Abstract [en]

    A new square-root algorithm for Kalman filtering and smoothing is derived. The new algorithm is a modification of the information filter presented by Paige and Saunders [C.C. Paige and M.A. Saunders, Least Squares Estimation of Discrete Linear Dynamic System Using Orthogonal Transformations, SIAM J. Num.Anal 12 (1977) pp. 180-193] and can be used when the input covariance matrices are diagonal. Potential ill-conditioning, caused by different sizes of the input covariances, is handled using techniques for solving weighted and constrained least squares problems. That is, the ordinary QR-decomposition that is used in the filter by Paige and Sauders are replaced by a weighted QR-decomposition introduced by Gulliksson and Wedin [M.G. Gulliksson and P.-Å. Wedin, Modyfying the QR Decomposition to Weighted and Constrained Linear Least Squares, SIAM J. Mat.Anal. 13 (1992) pp. 1298-1313]. This technique implies that the new algorithm can handle singular covariance matrices as well as singular information matrices.

  • 23. Söderkvist, Inge
    Computing parameters in nonlinear least squares models1993Doctoral thesis, comprehensive summary (Other academic)
  • 24.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Derivation of fixed interval smoothing formulas1996In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 9, no 2, p. 25-28Article in journal (Refereed)
    Abstract [en]

    It is shown that the derivation of the fixed interval smoothing formulas by M. R. Osborne and T. Prvan \ref[Appl. Math. Lett. 4 (1991), no. 2, 43--44] contains a mistake. A new and correct derivation, based on the same ideas of applying the projection theorem on Hilbert spaces of random variables, is given.

  • 25.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    En separat kurs för datorstödda matematikverktyg1999In: Datorstödd eller datorstörd matematikundervisning ?, Stockholm: Högskoleverket (Grundutbildningsrådet) , 1999, p. 122-125Chapter in book (Other (popular science, discussion, etc.))
  • 26.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Introductory overview of surface reconstruction methods1999Report (Other academic)
    Abstract [en]

    We consider the issue of constructing a digital model of a physicalsurface. An overview of fundamental methods is given. The methodsuse measurements of points on the surface in order to compute a mathematicalsurface representation that approximates the physical surface.Different surface representations are presented and algorithms that fitsuch representations to the measurements are outlined. We identifysome of the difficulties and pointers to the literature in the field aregiven.

  • 27.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On algorithms for generalized least squares problems with ill-conditioned covariance matrices1996In: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658, Vol. 11, p. 303-313Article in journal (Refereed)
    Abstract [en]

    The problem of computing estimates of parameters in linear models with additive noise and known ill-conditioned covariance matrix is considered. Some of the mostly used algorithms for solving the corresponding generalized least squares problem are discussed and complimentary numerical properties of the algorithms are exemplified. An algorithm, based on recent techniques for solving weighted and constrained least squares problems, is proposed. This algorithm handles both exact and diffuse information in an uniform framework and it shows to have superior numerical properties, compared to other frequently used algorithms, on some given examples.

  • 28.
    Söderkvist, Inge
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On Filter Algorithms for Computing Least Squares Splines1995Report (Other academic)
    Abstract [en]

    The problem of computing a least squares spline using Kalman filter algorithms is considered. An appropriate stochastic setting is identified and a new efficient algorithm, based on techniques for weighted and constrained linear least squares, is presented. Numerical examples illustrating good numerical properties of the new algorithm are given.

  • 29. Söderkvist, Inge
    Perturbation analysis of the orthogonal procrustes problem1993In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 33, no 4, p. 687-694Article in journal (Refereed)
    Abstract [en]

    Given two arbitrary real matrices A and B of the same size, the orthogonal Procrustes problem is to find an orthogonal matrix M such that the Frobenius norm ||MA - B|| is minimized. This paper treats the common case when the orthogonal matrix M is required to have a positive determinant. The stability of the problem is studied and suprem um results for the perturbation bounds are derived.

  • 30. Söderkvist, Inge
    Some numerical methods for kinematical analysis1990Licentiate thesis, comprehensive summary (Other academic)
  • 31.
    Söderkvist, Inge
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Gustafsson, Lennart
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
    On methods for computing rotations of spheres1994Report (Other academic)
    Abstract [en]

    Some numerical methods for calculating the rotation of a sphere with a dot pattern are studied. The moving sphere has been video recorded and the coordinates of the moving dots have been determined with the aid of image analysis. It turns out that a method that uses a least squares technique to compute the rotation matrix of the rotation is least sensitive to discretisation errors, but more traditionally methods, that use vector cross products, are more computationally efficient when less than five dots are available. 1 This work was supported by Norrbottens Forskningsrad, Lulea, Sweden 1 Introduction The movement of particles can be described as the sums of translations and a rotations. In experimental verification of mathematical models of granular flows it is therefore of importance to measure not only translation but also rotation. Such measurements are rare, however, and mostly deal with the rotation of a single or very few particles [2, 9]. This is easily explained by the com...

  • 32.
    Söderkvist, Inge
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedin, Per-Åke
    Department of Computing Science, Umeå University.
    On condition numbers and algorithms for determining a rigid body movement1994In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 34, no 3, p. 424-436Article in journal (Refereed)
    Abstract [en]

    Using a set of landmarks to represent a rigid body, a rotation of the body can be determined in the least-squares sense as the solution of an orthogonal Procrustes problem. We discuss some geometrical properties of the condition number for the problem of determining the orthogonal matrix representing the rotation. It is shown that the condition number depends critically on the configuration of the landmarks. The problem is also reformulated as an unconstrained nonlinear least-squares problem and the condition number is related to the geometry of such problems. In the common 3-D case, the movement can be represented by using a screw axis. Also the condition numbers for the problem of determining the screw axis representation are shown to depend closely on the configuration of the landmarks. The condition numbers are finally used to show that the algorithms used are stable.

  • 33. Söderkvist, Inge
    et al.
    Wedin, P.-Å.
    Determining the movements of the skeleton using well-configured markers1993In: Journal of Biomechanics, ISSN 0021-9290, E-ISSN 1873-2380, Vol. 26, p. 1473-1477Article in journal (Refereed)
    Abstract [en]

    The problem of determining skeletal movements in 3 dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in a least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of the landmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.

1 - 33 of 33
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf