Conjugate Gradient Methods for Toeplitz Systems

In this paper, we consider the solutions of symmetric positive definite, but ill-conditioned, Toeplitz systems A_n x = b. Here we propose to solve the system by the recursive-based preconditioned conjugate gradient method. The idea is to use the inverse of ...

We consider linear systems of equations arising from the sinc method of boundary value problems which are typically nonsymmetric and dense. For the solutions of these systems we propose Krylov subspace methods with banded preconditioners. We prove that ...

The preconditioned conjugate gradient (PCG) method is an effective means for solving systems of linear equations where the coefficient matrix is symmetric and positive definite. The incomplete $LDL^t $ factorizations are a widely used class of ...