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In this paper, we design a mixed double-multiple precision version of the hyperplane constrained method for singular value decomposition (SVD), which is based on solving nonlinear systems with the solutions constrained on hyperplanes. We also propose its hybrid method in order to shorten the running time. Through some numerical examples for matrices with small singular values, it is shown that, by new versions, the SVD is computable with high relative accuracy.

Mixed double-multiple precision version of hyperplane constrained method for singular value decomposition