Solving Large Sparse Systems of Equations by Iterative Methods

• Main Authors: Yi-Hung Ke, 柯宜宏
• Other Authors: Luhan Chuang
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/84188697217536667543

碩士 === 大同大學 === 應用數學研究所 === 89 === Each iterative method uses successive procedure to produce a more accurate solution to a linear system at each iteration. In this paper, we review some famous iterative methods such as IGCG, CGS, and BICGSTAB and discuss at what situation the breakdown will occur. We also choose two partial differential equations with boundary value conditions as our test problems and discretisize them to linear systems by the central difference. Furthermore, we choose some types of Krylov subspace methods to solve these test problems, and compare the computing time and the rate of convergence of those Krylov subspace methods.