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A singular value decomposition algorithm based on solving hyperplane constrained nonlinear systems |
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| Authors: | Kenichi Yadani Koichi Kondo |
| Institution: | a Graduate School of Informatics, Kyoto University, Yoshida-Hommachi, Sakyo-ku, Kyoto 606-8501, Japan b Faculty of Science and Engineering, Doshisha University, 1-3, Tatara Miyakodani, Kyotanabe City, Kyoto 610-0394, Japan c Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nagaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522, Japan |
| Abstract: | A new algorithm for singular value decomposition (SVD) is presented through relating SVD problem to nonlinear systems whose solutions are constrained on hyperplanes. The hyperplane constrained nonlinear systems are solved with the help of Newton’s iterative method. It is proved that our SVD algorithm has the quadratic convergence substantially and all singular pairs are computable. These facts are also confirmed by some numerical examples. |
| Keywords: | Singular value decomposition Newton&rsquo s iterative method Nonlinear system Hyperplane Quadratic convergence |
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