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.
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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.
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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.
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