id: 06063169
dt: j
an: 06063169
au: Pang, Hong-Kui; Zhang, Ying-Ying; Jin, Xiao-Qing
ti: Tri-diagonal preconditioner for pricing options.
so: J. Comput. Appl. Math. 236, No. 17, 4365-4374 (2012).
py: 2012
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: European call option; partial integro-differential equation; nonsymmetric
    Toeplitz system; normalized preconditioned system; tri-diagonal
    preconditioner; family of generating functions
ci: 
li: doi:10.1016/j.cam.2012.04.003
ab: Summary: The value of a contingent claim under a jump-diffusion process
    satisfies a partial integro-differential equation (PIDE). We localize
    and discretize this PIDE in space by the central difference formula and
    in time by the second order backward differentiation formula. The
    resulting system $T_n\bold {x}= \bold {b}$ in general is a nonsymmetric
    Toeplitz system. We then solve this system by the normalized
    preconditioned conjugate gradient method. A tri-diagonal preconditioner
    $L_{n}$ is considered. We prove that under certain conditions all the
    eigenvalues of the normalized preconditioned matrix
    $(L_n^{-1}T_n)^{\ast}(L_n^{-1}T_n)$ are clustered around one, which
    implies a superlinear convergence rate. Numerical results exemplify our
    theoretical analysis.
rv: