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arXiv · 1401.2350

A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix

Takumi Yamashita·Kinji Kimura·Yusaku Yamamoto
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Abstract

Traces of inverse powers of a positive definite symmetric tridiagonal matrix give lower bounds of the minimal singular value of an upper bidiagonal matrix. In a preceding work, a formula for the traces which gives the diagonal entries of the inverse powers is presented. In this paper, we present another formula which gives the traces based on a quite different idea from the one in the preceding work. An efficient implementation of the formula for practice is also presented.

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Takumi Yamashita, Kinji Kimura, Yusaku Yamamoto. 2014-01-10. A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix. https://arxiv.org/abs/1401.2350

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