Preconditioned gradient iterations for the eigenproblem of definite matrix pairs

Perturbation analysis for the eigenproblem of periodic matrix pairs

This paper is devoted to perturbation analysis for the eigenproblem of periodic matrix pairs {(Aj ,Ej )}j=1. We first study perturbation expansions of periodic deflating subspaces and eigenvalue pairs. Then, we derive explicit expressions of condition numbers, perturbation bounds and backward errors for eigenvalue pairs and periodic deflating subspaces. © 2001 Elsevier Science Inc. All rights r...

Preconditioned Lanczos Methods for the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix

In this paper, we apply the preconditioned Lanczos (PL) method to compute the minimum eigenvalue of a symmetric positive definite Toeplitz matrix. The sine transform-based preconditioner is used to speed up the convergence rate of the PL method. The resulting method involves only Toeplitz and sine transform matrix-vector multiplications and hence can be computed efficiently by fast transform al...

Analysis of preconditioned Picard iterations for the Navier-Stokes equations

Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations

Some techniques suitable to the control of the solution error in the Preconditioned Conjugate Method are considered and compared. The estimation can be performed both in the course ot the iterations and after their termination. The importance of such techniques follows from the non-existence of some reasonable a priori error estimate for very ill-conditioned linear systems when information abou...

Preconditioned Conjugate Gradient

.. ................................................................................................................... ix Chapter 1. Introduction ..................................................................................................1 Chapter 2. Background ..................................................................................................6 2.1. Matrix Compu...