A new block preconditioner for weighted Toeplitz regularized least-squares problems

Abstract

We introduce a new block preconditioner for the solution of weighted Toeplitz regularized least-squares problems written in augmented system form. The proposed preconditioner is obtained based on the new splitting of coefficient matrix which results in an unconditionally convergent stationary iterative method. Spectral analysis of the preconditioned matrix is investigated. In particular, we show that the preconditioned matrix has a very nice eigenvalue distribution which can lead to fast convergence of the preconditioned Krylov subspace methods such as GMRES. Numerical experiments are reported to demonstrate the performance of preconditioner used with GMRES method in the solution of augmented system form of weighted Toeplitz regularized least-squares problems.

Keywords:

• Preconditioning
• splitting
• least-squares problems
• weighted Toeplitz matrices

2010 AMS Subject Classifications:

• 65F10
• 65F50

Acknowledgments

The authors express their thanks to the referees for the comments and constructive suggestions, which were valuable in improving the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).