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Volume 1, Issue 1
Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

Hong-Kui Pang, Ying-Ying Zhang & Xiao-Qing Jin

DOI: 10.4208/eajam.260609.190510a

East Asian J. Appl. Math., 1 (2011), pp. 82-88.

Published online: 2018-02

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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

European call option, partial integro-differential equation, nonsymmetric Toeplitz system, normalized preconditioned system (matrix), tri-diagonal preconditioner.

  • AMS Subject Headings

65F10, 65M06, 91B70, 47B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-82, author = {Hong-Kui Pang, Ying-Ying Zhang and Xiao-Qing Jin}, title = {Tri-Diagonal Preconditioner for Toeplitz Systems from Finance}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {1}, pages = {82--88}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260609.190510a}, url = {http://global-sci.org/intro/article_detail/eajam/10897.html} }
TY - JOUR T1 - Tri-Diagonal Preconditioner for Toeplitz Systems from Finance AU - Hong-Kui Pang, Ying-Ying Zhang & Xiao-Qing Jin JO - East Asian Journal on Applied Mathematics VL - 1 SP - 82 EP - 88 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.260609.190510a UR - https://global-sci.org/intro/article_detail/eajam/10897.html KW - European call option, partial integro-differential equation, nonsymmetric Toeplitz system, normalized preconditioned system (matrix), tri-diagonal preconditioner. AB -

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.

Hong-Kui Pang, Ying-Ying Zhang and Xiao-Qing Jin. (2018). Tri-Diagonal Preconditioner for Toeplitz Systems from Finance. East Asian Journal on Applied Mathematics. 1 (1). 82-88. doi:10.4208/eajam.260609.190510a
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