Orthogonal projections are optimal algorithms

DOI10.1016/0021-9045(84)90018-2zbMath0531.41030OpenAlexW2090642700MaRDI QIDQ788227

Charles A. Micchelli

Publication date: 1984

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(84)90018-2

zbMATH Keywords

Gaussian measuresoptimal informationoptimal algorithmsHousholder transformationsinfinite dimensional Hilbert spaces

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Algorithms for approximation of functions (65D15)

Related Items

Orthogonally invariant measures and best approximation of linear operators, Random approximation of Sobolev embeddings, Linear widths of a multivariate function space equipped with a Gaussian measure, Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure, s-numbers in information-based complexity, Average case optimal algorithms in Hilbert spaces

Cites Work

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• Average case optimality for linear problems
• Gaussian measures in Banach spaces
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• Optimal Estimation of Linear Operators in Hilbert Spaces from Inaccurate Data