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Lanczos-Based Exponential Filtering for Discrete Ill-Posed Problems

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Abstract

We describe regularizing iterative methods for the solution of large ill-conditioned linear systems of equations that arise from the discretization of linear ill-posed problems. The regularization is specified by a filter function of Gaussian type. A parameter μ determines the amount of regularization applied. The iterative methods are based on a truncated Lanczos decomposition and the filter function is approximated by a linear combination of Lanczos polynomials. A suitable value of the regularization parameter is determined by an L-curve criterion. Computed examples that illustrate the performance of the methods are presented.

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Authors and Affiliations

  1. Department of Mathematics, Case Western Reserve University, Cleveland, OH, 44106, USA

    D. Calvetti

  2. Department of Mathematics and Computer Science, Kent State University, Kent, OH, 44242, USA

    L. Reichel

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  1. D. Calvetti
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  2. L. Reichel
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Calvetti, D., Reichel, L. Lanczos-Based Exponential Filtering for Discrete Ill-Posed Problems. Numerical Algorithms 29, 45–65 (2002). https://doi.org/10.1023/A:1014899604567

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