Approximation of generalized inverses by iterated regularization

DOI10.1080/01630567908816031zbMath0446.65026OpenAlexW2017439015MaRDI QIDQ3891688

David Chillingworth, J. Thomas King

Publication date: 1979

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630567908816031

zbMATH Keywords

regularizationclosed rangeMoore-Penrose generalized inverseuniform error boundspointwise error estimatesstability of the iteration

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical solutions to equations with linear operators (65J10) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

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Cites Work

• Unnamed Item
• Extrapolation and the method of regularization for generalized inverses
• New error bounds for the penalty method and extrapolation
• An iterative method for solving incorrectly posed problems