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 - <p style="text-align: justify;">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.</p>