Synthetical development of fast numerical methods for solving large-scale linear systems which arise g from the field of computational science and engineerin

本项目的目标是综合开发求解大规模线性方程组的快速数值方法，这些数值方法源于计算科学和工程领域。在整个项目中，我们基本完成了预定的目标。对大型线性系统的应用情况进行了全面的考察。从大小、结构和代数三个方面对线性系统的系数矩阵进行了分类。通过大量试题对新方法GPBi-CG(ω)和GPBi-CG的收敛性能进行了评价。研究了广义线性系统的收敛理论。研究了几种不同的预适应技术。提出了一种新的快速、基本的方法--BiCR法。为这项工程建造了一个新的并行计算机系统。一个新的大型线性系统的Web服务器系统即将建成。

The target of this project is synthetically to develop fast numerical methods for solving large-scale linear systems which arise from the field of computational science and engineering. Throughout the whole of this project, we completed almost the target.The research results of this project are concluded as follows.1. The circumstance of applications which lead large linear systems was investigated by all of numbers.2. The coefficient matrix of linear systems was classified from size, structure and algebra.3. The convergent property of new methods GPBi-CG(ω) and GPBi-CG was evaluated through many test problems.4. The convergence theory for singular linear systems was studied.5. Several kinds of preconditioning technique was studied.6. A new fast and basic method, so-called Bi-CR, was proposed.7. A new systems of parallel computer was built for this project.8. A new web server system for large linear system was built almost.