NAS2007では以下の招待講演を行います。
講演者：
Zhong-Zhi Bai ( Institute of Computational Mathematics and Scientific / Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
講演タイトル：
On Hermitian and skew-Hermitian splitting iteration methods.
講演者紹介：
Bai先生は数値線形代数の分野で中国で指導的立場にある若手の教授で、国際的にも活躍されています。
matrix-splittingによる反復法、前処理付きクリロフ部分空間法、行列方程式を初めとして幅広く研究されています。
講演アブストラクト：
The Hermitian and skew-Hermitian splitting (HSS) iteration scheme is an efficient and practical method for solving large sparse non-Hermitian system of linear equations.
In this talk, after reviewing the HSS iteration method and its basic convergence theory for non-Hermitian positive definite matrices, we give a sufficient and necessary condition for guaranteeing its convergence for nonsingular and non-Hermitian positive semidefinite matrices.
We then discuss the semi-convergence property of the HSS iteration method and derive a sufficient and necessary convergence condition for singular and non-Hermitian positive semidefinite matrices.
According to the optimal iteration parameter involved, we first compute it exactly for real two-by-two matrices, and then compute it exactly for special block two-by-two matrices.
These formulas are used to give estimation for the optimal iteration parameter of HSS iteration method for general non-Hermitian matrices.
Finally, some numerical results are used to examine the effectiveness of the HSS iteration method with the exact or the estimated optimal iteration parameter.
(2007/01/31更新)