A bound for norms of functions of matrices
β Scribed by N.J. Young
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 273 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
## Abstract We determine bounds for the spectral and π~__p__~ norm of CauchyβHankel matrices of the form __H__~__n__~=[1/(__g__+__h__(__i__+__j__))]^__n__^~__i,j__=1~β‘ ([1/(__g__+__kh__)]^__n__^~__i,j__=1~), __k__=0, 1,β¦, __n__ β1, where __k__ is defined by __i__+__j__=__k__ (mod __n__). Copyright
We define a region \(H_{\alpha, f}\) in the complex number field, where \(\alpha\) is a complex number, \(f(x) \in K[x]\) and \(f(\alpha) \neq 0\). The region \(H_{\alpha, f}\) contains no zeros of \(f(x)\) and is relatively easy to analyze. We analyze the region with respect to \(K=\mathbb{R}\) and