Different methods of orthogonal projection onto a hyperspace defined by n points in a Euclidean space of dimension n
Keywords:
Orthogonal projections, Hyperspace, Numerical Methods, MATLABAbstract
This article presents nine different methods of orthogonal projection onto a hyperspace defined by points. These methods have been implemented in MATLAB language. Comparisons have been made of numerical precision and cpu times, taking one of them as a reference. It has placed special emphasis on an inversion’s method with comments to its potential and some demonstrations that justify the intermediate steps used.
Downloads
Download data is not yet available.
References
[1] C. D. Meyer, Matrix Analysis and Applied Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics, 2000.
[2] J. A. Brandon and A. Cowley, ‘‘A weighted least squares method for circle fitting to frequency response data,’’ J. Sound and Vibrations, vol. 83, no. 3, pp. 419-424, 1983.
[3] D. E. Blair, Inversion theory and conformal mapping. Providence, RI: American Mathematical Society, 2000.
[4] G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” in Handbook for Automatic Computation, vol. 2 (Linear Algebra). New York: Springer-Verlag, pp. 134–151, 1971.
[5] J. W. Demmel, Applied Numerical Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics, 1997.
[6] F. P. Preparata and M. I. Shamos, Computational geometry: an introduction. New York: Springer-Verlag, 1985.
[2] J. A. Brandon and A. Cowley, ‘‘A weighted least squares method for circle fitting to frequency response data,’’ J. Sound and Vibrations, vol. 83, no. 3, pp. 419-424, 1983.
[3] D. E. Blair, Inversion theory and conformal mapping. Providence, RI: American Mathematical Society, 2000.
[4] G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” in Handbook for Automatic Computation, vol. 2 (Linear Algebra). New York: Springer-Verlag, pp. 134–151, 1971.
[5] J. W. Demmel, Applied Numerical Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics, 1997.
[6] F. P. Preparata and M. I. Shamos, Computational geometry: an introduction. New York: Springer-Verlag, 1985.
Downloads
Published
2015-11-02
How to Cite
[1]
J. Flaquer, “Different methods of orthogonal projection onto a hyperspace defined by n points in a Euclidean space of dimension n”, Memoria investig. ing. (Facultad Ing., Univ. Montev.), no. 13, pp. 33–48, Nov. 2015.
Issue
Section
Articles
License
Copyright (c) 2019 Juan Flaquer
This work is licensed under a Creative Commons Attribution 4.0 International License.
