97 research outputs found
Introduction to StarNEig -- A Task-based Library for Solving Nonsymmetric Eigenvalue Problems
In this paper, we present the StarNEig library for solving dense
non-symmetric (generalized) eigenvalue problems. The library is built on top of
the StarPU runtime system and targets both shared and distributed memory
machines. Some components of the library support GPUs. The library is currently
in an early beta state and only real arithmetic is supported. Support for
complex data types is planned for a future release. This paper is aimed for
potential users of the library. We describe the design choices and capabilities
of the library, and contrast them to existing software such as ScaLAPACK.
StarNEig implements a ScaLAPACK compatibility layer that should make it easy
for a new user to transition to StarNEig. We demonstrate the performance of the
library with a small set of computational experiments.Comment: 10 pages, 4 figures (10 when counting sub-figures), 2 tex-files.
Submitted to PPAM 2019, 13th international conference on parallel processing
and applied mathematics, September 8-11, 2019. Proceedings will be published
after the conference by Springer in the LNCS series. Second author's first
name is "Carl Christian" and last name "Kjelgaard Mikkelsen
Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously
Multi-shifted linear systems with non-Hermitian coefficient matrices arise in
numerical solutions of time-dependent partial/fractional differential equations
(PDEs/FDEs), in control theory, PageRank problems, and other research fields.
We derive efficient variants of the restarted Changing Minimal Residual method
based on the cost-effective Hessenberg procedure (CMRH) for this problem class.
Then, we introduce a flexible variant of the algorithm that allows to use
variable preconditioning at each iteration to further accelerate the
convergence of shifted CMRH. We analyse the performance of the new class of
methods in the numerical solution of PDEs and FDEs, also against other
multi-shifted Krylov subspace methods.Comment: Techn. Rep., Univ. of Groningen, 34 pages. 11 Tables, 2 Figs. This
manuscript was submitted to a journal at 20 Jun. 2016. Updated version-1: 31
pages, 10 tables, 2 figs. The manuscript was resubmitted to the journal at 9
Jun. 2018. Updated version-2: 29 pages, 10 tables, 2 figs. Make it concise.
Updated version-3: 27 pages, 10 tables, 2 figs. Updated version-4: 28 pages,
10 tables, 2 fig
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