Iterative Algorithms for Parallel Computers

这个项目的研究领域是在向量计算机和并行计算机上迭代求解大型空间线性方程组。这项研究的目标是开发适合于并行计算机并利用并行体系结构的特性的迭代算法。将研究三个特别的主题。首先，将开发和测试对称不确定系统的多项式预适应的自适应程序。其次，研究了矩阵的谱位于复平面上任意区域的非对称方程组的自适应多项式方法。第三个研究主题将是重新启动的广义共轭梯度算法的并行化，例如GMRES算法。每个研究主题的目标都是开发更适合高度并行体系结构的算法。

The area of research for this project is the iterative solution of large sparese linear systems of equations on vector and parallel computers. The goal of this research is to develop iterative algorithms which are adapted to parallel computers and which exploit the properties of parallel architectures. Three particular topics will be studied. First adaptive procedures for polynomial preconditioning of symmetric indefinite systems will be developed and tested. Second, research will be done on an adaptive polynomial method for solving nonsymmetric systems of equations for which the specturm of the matrix lies in an arbitrary region in the complex plane. A third topic of research will be the parallelization of restarted generalized conjugate gradient algorithms such as the GMRES algotithm. The goal of each of these topics of research is to develop algorithms which are better suited to highly parallel architectures.