Iterative Algorithms for Parallel Computers

本项目的研究领域是迭代求解 向量上的大型稀疏线性方程组 并行计算机 这项研究的目的是开发 适用于并行计算机的迭代算法， 其利用并行架构的特性。 三 将研究特定的主题。 第一个适应性程序， 对称不定系统的多项式预处理将 开发和测试。 第二，研究将在 求解非对称方程组的自适应多项式方法 矩阵的谱位于一个 复平面上的任意区域。 第三个研究课题 将是重新开始的广义共轭 梯度算法，如GMRES算法。 的目标 这些研究课题中的每一个都是为了开发算法， 更适合高度并行的架构。

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.