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An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure. (English) Zbl 1210.65091
Summary: This paper describes a new numerical method for the solution of large linear discrete ill-posed problems, whose matrix is a Kronecker product. Problems of this kind arise, for instance, from the discretization of Fredholm integral equations of the first kind in two space-dimensions with a separable kernel. The available data (right-hand side) of many linear discrete ill-posed problems that arise in applications is contaminated by measurement errors. Straightforward solution of these problems generally is not meaningful because of severe error propagation. We discuss how to combine the truncated singular value decomposition (TSVD) with reduced rank vector extrapolation to determine computed approximate solutions that are fairly insensitive to the error in the data. Exploitation of the structure of the problem keeps the computational effort quite small.

65F22 Ill-posedness and regularization problems in numerical linear algebra
65F20 Numerical solutions to overdetermined systems, pseudoinverses
45B05 Fredholm integral equations
65R20 Numerical methods for integral equations
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