Iterative Algorithms for Parallel Computers

本项目的研究领域是在矢量和并行计算机上求解大型稀疏线性方程组的迭代解。本研究的目标是开发适合并行计算机的迭代算法，并利用并行架构的特性。将研究三个特定的主题。首先自适应程序的多项式预处理对称不定系统将开发和测试。其次，研究求解矩阵谱位于复平面任意区域的非对称方程组的自适应多项式方法。第三个研究课题将是重新启动的广义共轭梯度算法（如GMRES算法）的并行化。这些研究主题的目标都是开发更适合高度并行架构的算法。

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.