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

Abstract

AbstractWe 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 (flexible) GMRES method in the solution of augmented system form of weighted Toeplitz regularized least-squares problems.Keywords: PreconditioningSplittingLeast-squares problemsWeighted Toeplitz matricesAMS classification 2010:: 65F1065F50DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors express their thanks to the referees for the comments and constructive suggestions, which were valuable in improving the quality of the manuscript.