Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse

被引：33

作者：

Rump, Siegfried M. ^{[1
,2
,3
]}

机构：

[1] Hamburg Univ Technol, Inst Reliable Comp, D-21071 Hamburg, Germany

[2] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

[3] Univ Paris 06, Dept Calcul Sci, Lab LIP6, F-75252 Paris 05, France

来源：

BIT NUMERICAL MATHEMATICS | 2011年 / 51卷 / 02期

关键词：

Spectral norm; Verification; Error bounds; Condition number; INTLAB; VERIFICATION; PROOF;

D O I：

10.1007/s10543-010-0294-0

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of a matrix are mandatory. We present various approaches to this together with some auxiliary useful estimates.

引用

页码：367 / 384

页数：18

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