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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1007/s00520-004-0609-2

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1572-9265

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Accelerated Landweber methods based on codilated

Authors: Wolfgang Erb
Publish Date: 2014/04/26
Volume: 68, Issue: 2, Pages: 229-260
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Abstract

In this article we introduce and study accelerated Landweber methods for linear illposed problems obtained by an alteration of the coefficients in the threeterm recurrence relation of the νmethods The residual polynomials of the semiiterative methods under consideration are linked to a family of codilated ultraspherical polynomials This connection makes it possible to control the decay of the residual polynomials at the origin by means of a dilation parameter Depending on the data the approximation error of the νmethods can be improved by altering this dilation parameter The convergence order of the new semiiterative methods turns out to be the same as the convergence order of the original νmethods The new algorithms are tested numerically and a simple adaptive scheme is developed in which an optimal dilation parameter is computed in every iteration step

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