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Optimal linear randomized methods for linear operators in Hilbert spaces

โœ Scribed by Erich Novak

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
576 KB
Volume
8
Category
Article
ISSN
0885-064X

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โœฆ Synopsis

Basic questions of information-based complexity are strongly related to n-widths and s-numbers. In this paper we study Monte Carlo methods or randomized methods for linear operators. Similar as in the worst case, Math6 defined linear stochastic n-widths. Our main result is the characterization of these widths in the case of linear operators in Hilbert spaces. o 1992 Academic press, IN.

๐Ÿ“œ SIMILAR VOLUMES

Linear fractional relations for Hilbert
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โœ V. A. Khatskevich; M. I. Ostrovskii; V. S. Shulman ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 207 KB ๐Ÿ‘ 1 views

## Abstract In this paper we study linear fractional relations defined in the following way. Let โ„‹๏ธ~__i__~ and โ„‹๏ธ~__i__~ ^โ€ฒ^, __i__ = 1, 2, be Hilbert spaces. We denote the space of bounded linear operators acting from โ„‹๏ธ~__j__~ to โ„‹๏ธ~__i__~ ^โ€ฒ^ by __L__ (โ„‹๏ธ~__j__~ , โ„‹๏ธ~__i__~ ^โ€ฒ^). Let __T__ โˆˆ