Numerical Linear Algebra and Eigenvalue Computations

研究者将研究求解中等到大规模特征值和广义特征值问题的数值算法。有两种研究方法。一是研究了一种新的可并行化的Hessenberg特征值算法，称为“细分-紧缩”。压缩细分算法降低了计算复杂度，提高了Hessenberg特征值问题的并行性。这有可能将海森伯格特征值问题的计算成本大大降低到当前水平以下。另一条研究路线涉及继续发展TTQRE，这是一种用于解决中等规模代数特征值问题的变体QR算法。尽管TTQRE已经证明了自己是传统QR算法的重大进步，但它还没有充分发挥其潜力。将设计在执行过程中动态调整其基本参数的策略。本项目资助一名研究生参与该项目的研究。学生的训练将受益于在真正的并行计算机上的实际计算经验，以及理论问题的工作。

The investigator will study numerical algorithms for solving moderate to large scale eigenvalue and generalized eigenvalue problems. There are two lines of research. One is to investigate a new kind of parallelizable Hessenberg eigen-value algorithm termed "subdivision-by-deflation". The subdivision-by-deflation algorithm reduces the computational complexity and increases the parallelism of Hessenberg eigenvalue problems. This has the potential of reducing the computational cost of the Hessenberg eigenvalue problem significantly below current levels.The other line of research involves continued development of TTQRE, a variant QR algorithm for solving the moderate scale algebraic eigenvalue problem. Although TTQRE has already proved itself to be a significant advance over traditional QR algorithms, it has not yet reached its full potential. Strategies will be designed that adjust its fundamental parameters dynamically during execution. This project supports a graduate student who will participate in the project. The student's training will benefit from practical computational experience on real parallel computers as from the work with theoretical problems.