Abstract
The generalized singular value decomposition (GSVD) is one of the essential tools in numerical linear algebra. This paper proposes a regularization method, combining Tikhonov regularization in general form with the truncated GSVD. Then the randomized algorithms are adopted to implement the truncation process. This randomized GSVD for the regularization of the large-scale ill-posed problems can achieve good accuracy with less computational time and memory requirement than the classical regularization methods. Finally, we present the error analyses for the randomized algorithms. Some illustrative numerical examples are provided.
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