Asymptotics of orthogonal polynomials and the numerical solution of ill-posed problems

DOI10.1007/BF02142497zbMath0851.65035MaRDI QIDQ1911450

Martin Hanke

Publication date: 26 November 1996

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

convergenceconjugate gradient methoditerative methodslinear ill-posed problemsChristoffel functionszeros of orthogonal polynomialscompact operator equationsmodified Lommel polynomialsTricomi-Carlitz polynomialsBrakhage's \(\nu\)-method

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (1)

Accelerated Landweber methods based on co-dilated orthogonal polynomials

Cites Work

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• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• Accelerated Landweber iterations for the solution of ill-posed equations
• An optimal stopping rule for the \(v\)-method for solving ill-posed problems, using Christoffel functions
• Fast decreasing polynomials
• Orthogonal polynomials suggested by a queueing model
• An $\epsilon $-Free a Posteriori Stopping Rule for Certain Iterative Regularization Methods
• Christoffel functions and orthogonal polynomials for exponential weights on [-1,1]

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