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Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-7566-3656
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-3811-062X
2012 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, no 3, p. 571-588Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
2012. Vol. 52, no 3, p. 571-588
Keywords [en]
Mathematics
Keywords [sv]
numerik, Matematik
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:ltu:diva-8758DOI: 10.1007/s10543-012-0371-7ISI: 000308234600004Scopus ID: 2-s2.0-84865746930Local ID: 74aec6df-c813-471b-a9b5-df74c969c19bOAI: oai:DiVA.org:ltu-8758DiVA, id: diva2:981696
Note
Validerad; 2012; 20120130 (berper)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Bergström, PerEdlund, OveSöderkvist, Inge

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