Tri-Diagonal Preconditioner for Toeplitz Systems from Finance
Hong-Kui Pang 1*, Ying-Ying Zhang 1, Xiao-Qing Jin 11 Department of Mathematics, University of Macau, Macao.
Received 26 June 2009; Accepted (in revised version) 19 May 2010
Available online 26 October 2010
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
Email: email@example.com (H.-K. Pang)