Approximate Solution Of Non Symmetric Generalized Eigenvalue Problems And Linear Matrix Equations On Hpc Platforms

Approximate Solution of Non-Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on HPC Platforms

The solution of the generalized eigenvalue problem is one of the computationally most challenging operations in the field of numerical linear algebra. A well known algorithm for this purpose is the QZ algorithm. Although it has been improved for decades and is available in many software packages by now, its performance is unsatisfying for medium and large scale problems on current computer architectures. In this thesis, a replacement for the QZ algorithm is developed. The design of the new spectral divide and conquer algorithms is oriented towards the capabilities of current computer architectures, including the support for accelerator devices. The thesis describes the co-design of the underlying mathematical ideas and the hardware aspects. Closely connected with the generalized eigenvalue value problem, the solution of Sylvester-like matrix equations is the concern of the second part of this work. Following the co-design approach, introduced in the first part of this thesis, a flexible framework covering (generalized) Sylvester, Lyapunov, and Stein equations is developed. The combination of the new algorithms for the generalized eigenvalue problem and the Sylvester-like equation solves problems within an hour, whose solution took several days incorporating the QZ and the Bartels-Stewart algorithm.

Computer & Control Abstracts

Vector and Parallel Processing - VECPAR 2000

This book is the ?nal outcome of VECPAR 2000 – 4th International Meeting on Vector and Parallel Processing. VECPAR constitutes a series of conferences, which have been organized by the Faculty of Engineering of the University of Porto since 1993, with the main objective of disseminating new knowledge on parallel computing. Readership of This Book The book is aimed at an audience of researchers and graduate students in a broad range of scienti?c areas, including not only computer science, but also applied mathematics and numerical analysis, physics, and engineering. Book Plan From a total of 66 papers selected on the basis of extended abstracts for p- sentation at the conference, a subset of 34 papers were chosen during a second review process leading to their inclusion in the book, together with the invited talks. The book contains a total of 40 papers organized into 6 chapters, where each may appeal to people in di?erent but still related scienti?c areas. All ch- ters, with the exception of Chapter 6, are initiated by a short text, providing a quick overview of the organization and papers in the chapter. The 13 papers in Chapter 1 cover the aspects related to the use of multiple processors. Operating systems, languages and software tools for scheduling, and code transformation are the topics included in this chapter, initiated by the talk on computing over the Internet, entitled Grid Computing,byIan Foster.