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On matrices for which norm bounds are attained

✍ Scribed by Hans Schneider; Hans F. Weinberger

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
869 KB
Volume
275-276
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let IIAllp,q be the norm induced on the matrix A with n rows and m columns by the Hijlder lP and d, norms on R" and Rm (or C" and C"'), respectively. It is easy to find an upper bound for the ratio llA/l,,/ilA &y. In this paper we study the classes of matrices for which the upper bound is attained. We shall show that for fixed A, attainment of the bound depends only on the signs of r -p and sq. Various criteria depending on these signs are obtained. For the special case p = q = 2, the set of all matrices for which the bound is attained is generated by means of singular value decompositions.

πŸ“œ SIMILAR VOLUMES

A note on bound for norms of Cauchy–Hank
A note on bound for norms of Cauchy–Hankel matrices
✍ SΓΌleyman Solak; Durmuş Bozkurt πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 77 KB

## Abstract We determine bounds for the spectral and 𝓁~__p__~ norm of Cauchy–Hankel matrices of the form __H__~__n__~=[1/(__g__+__h__(__i__+__j__))]^__n__^~__i,j__=1~≑ ([1/(__g__+__kh__)]^__n__^~__i,j__=1~), __k__=0, 1,…, __n__ –1, where __k__ is defined by __i__+__j__=__k__ (mod __n__). Copyright