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**Harvard**

Maclean, W. och Thomée, V. (2011) *Iterative methods for shifted positive definite linear systems and time discretization of the heat equation*.

** BibTeX **

@unpublished{

Maclean2011,

author={Maclean, W. and Thomée, Vidar},

title={Iterative methods for shifted positive definite linear systems and time discretization of the heat equation},

abstract={In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive definite matrix with a complex shift, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algorithm, and then a conjugate gradient method as well as a preconditioned version thereof.},

year={2011},

keywords={Laplace transform, finite elements, quadrature, Richardson iteration, conjugate gradient method, preconditioning.},

note={35},

}

** RefWorks **

RT Unpublished Material

SR Electronic

ID 155437

A1 Maclean, W.

A1 Thomée, Vidar

T1 Iterative methods for shifted positive definite linear systems and time discretization of the heat equation

YR 2011

AB In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive definite matrix with a complex shift, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algorithm, and then a conjugate gradient method as well as a preconditioned version thereof.

LA eng

LK http://arxiv.org/abs/1111.5105

OL 30