Developing iterative algorithms to solve Sylvester tensor equations

作者：

Highlights：

• We in this paper propose the bi-conjugate gradient and bi-conjugate residual methods in their tensor forms for solving the Sylvester tensor equation.

• BiCG-BTF and BiCR-BTF methods are superior to the modified conjugate gradient method in terms of both the number of iteration steps and CPU time.

• From the nearest Kronecker product, the convergence rate of the preconditioned BiCG-BTF and BiCR-BTF methods is about twice that of the PGMRES-BTF method.

摘要

•We in this paper propose the bi-conjugate gradient and bi-conjugate residual methods in their tensor forms for solving the Sylvester tensor equation.•BiCG-BTF and BiCR-BTF methods are superior to the modified conjugate gradient method in terms of both the number of iteration steps and CPU time.•From the nearest Kronecker product, the convergence rate of the preconditioned BiCG-BTF and BiCR-BTF methods is about twice that of the PGMRES-BTF method.

论文关键词：Sylvester tensor equation,Bi-conjugate gradient,Bi-conjugate residual,Tensor forms,Nearest Kronecker product

论文评审过程：Received 28 December 2020, Revised 11 April 2021, Accepted 23 May 2021, Available online 12 June 2021, Version of Record 12 June 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126403