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APARAMETERIZEDLOWERBOUNDFORTHESMALLESTSINGULARVALUE ELA

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ELA

A PARAMETERIZED LOWER BOUND FOR THE SMALLEST SINGULAR VALUE

∗

WEI ZHANG†, ZHENG-ZHI HAN†, AND SHU-QIAN SHEN‡

Abstract. This paper presents a parameterized lower bound for the smallest singular value of a matrix based on a new Gerˇsgorin-type inclusion region that has been established recently by these authors. The comparison of the new lower bound with known ones is supplemented with a numerical example.

Key words. Eigenvalue, Inclusion region, Smallest singular value, Lower bound.

AMS subject classifications.15A12, 65F15.

∗Received by the editors August 14, 2008. Accepted for publication September 26, 2008. Handling Editor: Roger A. Horn.

†School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China ([email protected]).

‡School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 17, pp. 487-492, October 2008

http://math.technion.ac.il/iic/ela

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