A Continuation Approach to Eigenvalue Problems

特征值问题的连续方法

• 批准号: 9103296
• 负责人: Hong Zhang
• 金额: $ 4.68万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1994-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103296&HistoricalAwards=false
• 关键词: Continuation; Approach; Eigenvalue; Problems

This project will investigate new eigenvalue algorithms based upon the idea of homotopy continuation. These consist of deforming a simple matrix into the matrix in question, while following the easily found eigenpairs of the simple matrix to the eigenpairs being sought. The issues to be studied include: - Further exploration of a recently developed continuation algorithm for eigenvalue problems of symmetric triadiagonal matrices. - Continuation algorithms for eigenvalue problems of large sparse matrices. - Parallelization and vectorization of such algorithms for a variety of advanced architectures. - Continuation algorithms for eigenvalue problems of nonsymmetric matrices. The emphasis will be on the development of efficient computational algorithms and their numerical implementation. Hopefully, the work will lead to software packages that can be applied to practical eigenvalue problems, especially those of large, sparse matrices.

该项目将研究基于同伦延拓思想的新特征值算法。 这些包括将简单矩阵变形为所讨论的矩阵，同时遵循简单矩阵的容易找到的特征对到正在寻找的特征对。 要研究的问题包括： - 进一步探索最近开发的对称三对角矩阵特征值问题的连续算法。 - 大型稀疏矩阵特征值问题的延拓算法。 - 针对各种高级架构的此类算法的并行化和矢量化。 - 非对称矩阵特征值问题的延拓算法。 重点将放在高效计算算法及其数值实现的开发上。 希望这项工作能够产生可应用于实际特征值问题的软件包，尤其是大型稀疏矩阵的特征值问题。