Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Simplified GSVD computations for the solution of linear discrete ill-posed problems
Journal of Computational and Applied Mathematics
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The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for problems of small to moderate size, which allow evaluation of the singular value decomposition of the matrix defining the problem, are the truncated singular value decomposition and Tikhonov regularization. The present paper proposes a novel choice of regularization matrix for Tikhonov regularization that bridges the gap between Tikhonov regularization and truncated singular value decomposition. Computed examples illustrate the benefit of the proposed method.