A Proposal for Toeplitz Matrix Calculations 论文

详细信息

发表期刊/会议

Studies in Applied Mathematics

发表日期

1986-04-01

发表年份

1986

摘要

In contrast to the usual (and successful) direct methods for Toeplitz systems Ax = b , we propose an algorithm based on the conjugate gradient method. The preconditioner is a circulant, so that all matrices have constant diagonals and all matrix‐vector multiplications use the Fast Fourier Transform. We also suggest a technique for the eigenvalue problem, where current methods are less satisfactory. If the first indications are supported by further experiment, this new approach may have useful applications—including nearly Toeplitz systems, and parallel computations.