Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Toeplitz Matrix Inversion: The Algorithm of W. F. Trench
Journal of the ACM (JACM)
A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications
A Superfast Toeplitz Solver with Improved Numerical Stability
SIAM Journal on Matrix Analysis and Applications
On the Compression of Low Rank Matrices
SIAM Journal on Scientific Computing
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
A direct method to solve block banded block Toeplitz systems with non-banded Toeplitz blocks
Journal of Computational and Applied Mathematics
A new algorithm for solving nearly penta-diagonal Toeplitz linear systems
Computers & Mathematics with Applications
| Hi-index | 0.09 |
We propose a ''fast'' algorithm for the construction of a data-sparse inverse of a generalToeplitz matrix. The computational cost for inverting an N x N Toeplitz matrix equals the cost of four length-N FFTs plus an O(N)-term. This cost should be compared to the O(N log^2N) cost of previously published methods. Moreover, while those earlier methods are based on algebraic considerations, the procedure of this paper is analysis-based; as a result, its stability does not depend on the symmetry and positive-definiteness of the matrix being inverted. The performance of the scheme is illustrated with numerical examples.