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Pivoted Cauchy-Like Preconditioners for Regularized Solution of Ill-Posed Problems

1999
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SIAM Journal on Scientific Computing
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Many ill-posed problems are solved using a discretization that results in a least squares problem or a linear system involving a Toeplitz matrix. The exact solution to such problems is often hopelessly contaminated by noise, since the discretized problem is quite ill-conditioned, and noise components in the approximate null-space dominate the solution vector. Therefore we seek an approximate solution that does not have large components in these directions. We use a preconditioned conjugate

doi:10.1137/s1064827596308974
fatcat:junqmgz52vdhbcvhuxpbglueie