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Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

Published online by Cambridge University Press:  28 May 2015

Hong-Kui Pang ,
Ying-Ying Zhang  and
Xiao-Qing Jin
Hong-Kui Pang*
Affiliation:
Department of Mathematics, University of Macau, Macao
Ying-Ying Zhang
Affiliation:
Department of Mathematics, University of Macau, Macao
Xiao-Qing Jin
Affiliation:
Department of Mathematics, University of Macau, Macao
*
Corresponding author. Email: ya87402@umac.mo
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Abstract

We consider a nonsymmetric Toeplitz system which arises in the discretization of a partial integro-differential equation in option pricing problems. The preconditioned conjugate gradient method with a tri-diagonal preconditioner is used to solve this system. Theoretical analysis shows that under certain conditions the tri-diagonal preconditioner leads to a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

Keywords

65F1065M0691B7047B35European call optionpartial integro-differential equationnonsymmetric Toeplitz systemnormalized preconditioned system (matrix)tri-diagonal preconditioner
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 1 , February 2011 , pp. 82 - 88
Copyright
Copyright © Global-Science Press 2011

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