East Asian Journal on Applied Mathematics, 1 (2011), pp. 82-88.


Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

Hong-Kui Pang 1*, Ying-Ying Zhang 1, Xiao-Qing Jin 1

1 Department of Mathematics, University of Macau, Macao.

Received 26 June 2009; Accepted (in revised version) 19 May 2010
Available online 26 October 2010
doi:10.4208/eajam.260609.190510a
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.

AMS subject classifications: 65F10, 65M06, 91B70, 47B35
Key words: European call option, partial integro-differential equation, nonsymmetric Toeplitz system, normalized preconditioned system (matrix), tri-diagonal preconditioner
*Corresponding author.
Email: ya87402@umac.mo (H.-K. Pang)
 

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