The Modified Truncated SVD Method for Regularization in General Form

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Abstract
The truncated singular value decomposition (SVD) method is useful for solving the standard-form regularization problem: min parallel-to x parallel-to 2 subject to min parallel-to Ax - b parallel-to 2. This paper presents a modification of the truncated SVD method, which solves the more general problem: min parallel-to Lx parallel-to 2 subject to min parallel-to Ax - b parallel-to 2, where L is a general matrix with full row rank. The extra work, associated with the introduction of the matrix L, is dominated by a QR-factorization of a matrix with dimensions smaller than those of L. In order to determine the optimal solution, it is often necessary to compute a sequence of regularized solutions, and it is shown how this can be accomplished with little extra computational effort. Finally, the new method is illustrated with an example from helioseismology.

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