Two iterative formulas of largest and smallest singular value of nonsingular matrices
Shun Xu
TL;DR
This paper introduces iterative formulas that efficiently approximate the largest and smallest singular values of nonsingular matrices, with proven convergence properties.
Contribution
The paper presents new iterative formulas for computing the extremal singular values of nonsingular matrices, enhancing existing methods with proven convergence.
Findings
Iterative formula for smallest singular value
Iterative formula for largest singular value
Convergence of the formulas
Abstract
We obtain an iterative formula that converges incrementally to the smallest singular value. Similarly, we obtain an iterative formula that converges decreasingly to the largest singular value.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Mathematical Inequalities and Applications