Construction, analysis and implementation of iterative methods for large systems of linear equations

大型线性方程组迭代方法的构造、分析和实现

• 批准号: 5210098
• 负责人: Professor Dr. Jörg Liesen
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 财政年份: 1999
• 资助国家: 德国
• 起止时间: 1998-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5210098?language=en
• 关键词: Construction; analysis; implementation; iterative; methods

Proposed is research in the areas of numerical linearalgebra and scientific computing. The focus is on Krylov subspacemethods, an important and widely used class of iterative methodsfor solving large and sparse linear algebraic systems. The lasttwo decades have seen an explosion of research activity on thesemethods which was spurred by the need to solve systems of vastlyincreasing dimensions in many areas of science and engineering.This development was mainly devoted to theconstruction rather than the analysis of methods. We intend to improve the understanding of the principles behind Krylov subspace methods particularly for nonsymmetric linear systems and thereby tocontribute to a much needed thorough analyticfoundation. While the analysis of Krylov subspace methods isinteresting from a mathematical point of view, it is alsoessential for the success of the methods in practice. We wantto utilize new insights for solving linear systems arising inseveral real-world and large-scale applications, includingconstraint optimization and radiation transportproblems. Simultaneously, the applications will guide us in ourtheoretical work.

提出了在数值线性代数和科学计算领域的研究。重点研究了Krylov子空间方法，它是求解大型稀疏线性代数系统的一类重要且广泛使用的迭代方法。在过去的二十年里，在科学和工程的许多领域中，由于需要解决规模越来越大的系统，对这些方法的研究活动呈爆炸式增长。这一发展主要致力于构造而不是方法的分析。我们打算提高对Krylov子空间方法背后的原理的理解，特别是对于非对称线性系统，从而为非常需要的彻底的分析基础做出贡献。虽然Krylov子空间方法的分析从数学角度来看很有趣，但它也是这些方法在实践中取得成功的关键。我们希望利用新的见解来解决一些现实世界和大规模应用中出现的线性系统，包括约束优化和辐射传输问题。同时，这些应用将指导我们的理论工作。