MENÜ MENÜ  

cover

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

Martin Köhler

ISBN 978-3-8325-5434-7
241 pages, year of publication: 2022
price: 51.50 €
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.

cover cover cover cover cover cover cover cover cover
Table of contents (PDF)

Preview (PDF)

Keywords:

  • Eigenwertprobleme
  • Matrixgleichungen
  • GPU-Beschleunigung
  • Divide-and-Conquer Algorithmen
  • Numerische Lineare Algebra

BUYING OPTIONS

51.50 €
in stock

44.00 €
61.50 €
65.50 €

(D) = Within Germany
(W) = Abroad

*You can purchase the eBook (PDF) alone or combined with the printed book (eBundle). In both cases we use the payment service of PayPal for charging you - nevertheless it is not necessary to have a PayPal-account. With purchasing the eBook or eBundle you accept our licence for eBooks.

For multi-user or campus licences (MyLibrary) please fill in the form or write an email to order@logos-verlag.de