An improvement of methods for solving the CUPL-Toeplitz linear system

In this paper, matrix order-reduction algorithms are realized to solve the CUPL-Toeplitz linear system. Firstly, we describe order-reduction algorithms for the multiplication of real skew-circulant matrix or complex circulant matrix and vector. Secondly, based on the two fast approaches [1] through splitting the CUPL-Toeplitz matrix into a Toeplitz matrix subtract a low-rank matrix, we propose new fast Toeplitz solvers to reduce the amount of calculation. Finally, numerical experiments are given to show the performance of the proposed algorithms. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper implements matrix order-reduction algorithms to solve the CUPL-Toeplitz linear system. Firstly, order-reduction algorithms for the multiplication of real skew-circulant matrix or complex circulant matrix and vector are described. Secondly, based on two fast approaches [1] by splitting the CUPL-Toeplitz matrix into a Toeplitz matrix subtracting a low-rank matrix, new fast Toeplitz solvers are proposed to reduce the amount of calculation. Finally, numerical experiments are conducted to demonstrate the performance of the proposed algorithms.