Volume 65, pp. 500-516, 2026.

Combined bounds for the standard and generalized singular value decompositions

Xiao Shan Chen, Xue Qing Zou, and Seak-Weng Vong

Abstract

In this paper, we present some new combined bounds for the standard singular value decomposition, extending some existing results. Furthermore, a combined perturbation bound for the generalized singular value decomposition of Grassmann matrix pairs is given, from which we obtain a Hoffman–Wielandt-type bound for generalized singular values.

Full Text (PDF) [280 KB], BibTeX , DOI: 10.1553/etna_vol65s500

Key words

combined bounds, standard singular value decomposition, generalized singular value decomposition, Frobenius norm

AMS subject classifications

65F15, 65F99

Links to the cited ETNA articles

[6]	Vol. 28 (2007-2008), pp. 16-39 Michele Benzi and Nader Razouk: Decay bounds and $O$($n$) algorithms for approximating functions of sparse matrices