Computations of Nonsymmetric Eigenvalue Problems and the Generalized Singular Value Decomposition

随着先进的计算设施和 浮点运算环境的改进， 进一步发展和分析的需要和机会 精确、稳定和高效的数值解， 数值线性代数问题 这项建议涉及到 几个基本的矩阵计算问题，如计算 大型非对称矩阵的特征值，计算不变量 具有特定谱的子空间， 非对称特征值问题，并计算广义QR 分解和广义奇异值分解。 的 研究的目标是开发高效的算法和可移植的 高性能计算机的软件， 这些问题在科学计算和其他领域的应用 数值分析领域。

With the availability of advanced computing facilities and the improvement of the environment of floating point arithmetic, there is a need and an opportunity for further development and analysis of accurate, stable and efficient numerical solutions for many numerical linear algebra problems. This proposal is concerned with several fundamental matrix computation problems, such as computing eigenvalues of large nonsymmetric matrices, computing invariant subspaces with specific spectra, estimating condition numbers of the nonsymmetric eigenvalue problem, and computing the generalized QR factorization and the generalized singular value decomposition. The goal of the research is to develop efficient algorithms and portable software for high- performance computers, motivated by many applications of these problems in scientific computing and other areas of numerical analysis.