Approximations of Extremal Eigenspace and Orthonormal Polar Factor
Ren-Cang Li
TL;DR
This paper addresses two key problems in matrix analysis: approximating extremal eigenspaces of Hermitian matrices and the orthonormal polar factor of general matrices, providing tight error bounds for these approximations.
Contribution
It introduces new tight error bounds for approximating eigenspaces and the polar factor, advancing understanding of matrix approximation accuracy.
Findings
Derived tight error bounds for eigenspace approximation.
Established bounds for orthonormal polar factor approximation.
Enhanced theoretical understanding of matrix approximation errors.
Abstract
This paper is concerned with two extremal problems from matrix analysis. One is about approximating the top eigenspaces of a Hermitian matrix and the other one about approximating the orthonormal polar factor of a general matrix. Tight error bounds on the quality of the approximations are obtained.
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Taxonomy
TopicsMatrix Theory and Algorithms · Statistical and numerical algorithms · Tensor decomposition and applications