Tikhonov regularization with MTRSVD method for solving large-scale discrete ill-posed problems

Regularization is possibly the most popular method for solving discrete ill-posed prob-lems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for large Tikhonov regularization in standard form. The proposed TR-MTRSVD algorithm introduces the idea of randomized algorithm into the improved truncated singular value decomposition (MTSVD) method to solve large Tikhonov regularization problems. The approximation matrix A & SIM;l produced by randomized SVD is replaced by the closest matrix A & SIM;k & SIM; in a unitarily invariant matrix norm with the same spectral condition number. The regularization parameters are determined by the discrepancy principle. Numerical examples show the effectiveness and efficiency of the proposed TR-MTRSVD algorithm for large Tikhonov regularization problems. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for solving large Tikhonov regularization problems. Numerical examples demonstrate the effectiveness and efficiency of the proposed method in regularization.