Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications [article]

Clarissa Garvey, Chang Meng, James G. Nagy
2018 arXiv   pre-print
In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large number of singular values and vectors more efficiently than other well known schemes, such as randomized matrix algorithms or iterative algorithms based on Golub-Kahan bidiagonalization. We provide theoretical results and numerical experiments to demonstrate the
more » ... accuracy of our approximation and show how the approximation can be used to solve large scale ill-posed inverse problems, either as an approximate filtering method, or as a preconditioner to accelerate iterative algorithms.
arXiv:1803.11525v2 fatcat:lvvv4j47sfeq3chmxcx66p2uiq