TY - JOUR T1 - Tri-Diagonal Preconditioner for Toeplitz Systems from Finance 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.