Displaying similar documents to “Some insights into the regularization of ill-posed problems.”

Residual norm behavior for Hybrid LSQR regularization

Havelková, Eva, Hnětynková, Iveta

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Hybrid LSQR represents a powerful method for regularization of large-scale discrete inverse problems, where ill-conditioning of the model matrix and ill-posedness of the problem make the solutions seriously sensitive to the unknown noise in the data. Hybrid LSQR combines the iterative Golub-Kahan bidiagonalization with the Tikhonov regularization of the projected problem. While the behavior of the residual norm for the pure LSQR is well understood and can be used to construct a stopping...

On the choice of subspace for iterative methods for linear discrete ill-posed problems

Daniela Calvetti, Bryan Lewis, Lothar Reichel (2001)

International Journal of Applied Mathematics and Computer Science

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Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.