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Regularized linear inversion with randomized singular value decomposition

Ito, K; Jin, B; (2020) Regularized linear inversion with randomized singular value decomposition. In: Mathematical and Numerical Approaches for Multi-Wave Inverse Problems. (pp. 45-72). Springer: Cham, Switzerland.

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Abstract

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value decomposition, Tikhonov regularization, and general Tikhonov regularization with a smoothness penalty. One distinct feature of the proposed approach is that it explicitly preserves the structure of the regularized solution in the sense that it always lies in the range of a certain adjoint operator. We provide error estimates between the approximation and the exact solution under canonical source condition, and interpret the approach in the lens of convex duality. Extensive numerical experiments are provided to illustrate the efficiency and accuracy of the approach.

Type: Book chapter
Title: Regularized linear inversion with randomized singular value decomposition
ISBN-13: 9783030486334
DOI: 10.1007/978-3-030-48634-1_5
Publisher version: https://doi.org/10.1007/978-3-030-48634-1_5
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10109215
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