Norm Invariance of Minimax Interpolation

N. Parker Willis; Yoram Bresler

doi:10.1109/18.135664

Norm Invariance of Minimax Interpolation

Research output: Contribution to journal › Article › peer-review

Abstract

Minimax-optimal interpolation algorithms minimize the error resulting from the worst signal from an allowable class. The result is presented that if this class lies in a Hilbert space, the minimax-optimal algorithm is independent of or invariant to the error norm. The result encompasses a broad class of inverse problems.

Original language	English (US)
Pages (from-to)	1177-1181
Number of pages	5
Journal	IEEE Transactions on Information Theory
Volume	38
Issue number	3
DOIs	https://doi.org/10.1109/18.135664
State	Published - May 1992

Keywords

Hilbert space
Optimal interpolation
approximation
inverse-problems
pseudo-inverse

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Online availability

10.1109/18.135664

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title = "Norm Invariance of Minimax Interpolation",

abstract = "Minimax-optimal interpolation algorithms minimize the error resulting from the worst signal from an allowable class. The result is presented that if this class lies in a Hilbert space, the minimax-optimal algorithm is independent of or invariant to the error norm. The result encompasses a broad class of inverse problems.",

keywords = "Hilbert space, Optimal interpolation, approximation, inverse-problems, pseudo-inverse",

author = "Willis, {N. Parker} and Yoram Bresler",

note = "Funding Information: Manuscript received May 15, 1991. N. P. Willis was supported by the Joint Services Electronic Program, Grant No. N 0014-90-J-1270. Y. Bresler was supported by the Joint Services Electronic Program, Grant No. N00014-90-J-1270 and in part by the National Science Foundation, Grant No. MIP88-10412 . The authors are with the Coordinated Scier,ce Lab, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1101 W. Springfield Avenue, Urbana, IL 61801. IEEE Log Number 9105771.",

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KW - pseudo-inverse

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Norm Invariance of Minimax Interpolation

Abstract

Keywords

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