Name: Approximate Solution of Non-Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on hpc Platforms (en Inglés)
Price: 121.06 USD
Availability: InStock
Author: Martin Kohler
ISBN: 9783832554347

portada Approximate Solution of Non-Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on hpc Platforms (en Inglés)

Approximate Solution of Non-Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on hpc Platforms (en Inglés)

Formato

Libro Físico

Editorial

Logos Verlag Berlin

Autor

Martin Kohler

Idioma

Inglés

N° páginas

241

Encuadernación

Tapa Blanda

ISBN13

9783832554347

Approximate Solution of Non-Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on hpc Platforms (en Inglés)

Martin Kohler (Autor) · Logos Verlag Berlin · Tapa Blanda

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Reseña del libro "Approximate Solution of Non-Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on hpc Platforms (en Inglés)"

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.