Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

Preconditioned Iterative Methods for Weighted Toeplitz Least Square Problems

Fast Iterative Methods for Solving Toeplitz-plus-hankel Least Squares Problems∗

In this paper, we consider the impulse responses of the linear-phase filter whose characteristics are determined on the basis of an observed time series, not on a prior specification. The impulse responses can be found by solving a least squares problem min ‖d − (X1 + X2)w‖2 by the fast Fourier transform (FFT) based preconditioned conjugate gradient method, for (M +2n−1)by-n real Toeplitz-plus-...

Some Results on New Preconditioned Generalized Mixed-Type Splitting Iterative Methods

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally...

Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems

We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerica...

Preconditioning Methods for Shift-Variant Image Reconstruction

Preconditioning methods can accelerate the convergence of gradient-based iterative methods for tomographic image reconstruction and image restoration. Circulant preconditioners have been used extensively for shiftinvariant problems. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. For inverse p...