A singular value decomposition algorithm based on solving hyperplane constrained nonlinear systems

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.