Lanczos-Based Exponential Filtering for Discrete Ill-Posed Problems |
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Authors: | D Calvetti L Reichel |
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Institution: | (1) Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA;(2) Department of Mathematics and Computer Science, Kent State University, Kent, OH 44242, USA |
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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 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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Keywords: | iterative method regularization exponential filter function |
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