Numerical Linear Algebra and Eigenvalue Computations

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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.