Efficiency improving implementation techniques for large scale matrix equation solvers
We address the important field of large scale matrix based algorithms in control and model order reduction. Many important tools from theory and applications in systems theory have been widely ignored during the recent decades in the context of PDE constraint optimal control problems and simulation...
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Technische Universität Chemnitz
2010
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ndltd-DRESDEN-oai-qucosa-de-qucosa-193352021-03-30T05:06:00Z Efficiency improving implementation techniques for large scale matrix equation solvers urn:nbn:de:bsz:ch1-201000843 1864-0087 eng We address the important field of large scale matrix based algorithms in control and model order reduction. Many important tools from theory and applications in systems theory have been widely ignored during the recent decades in the context of PDE constraint optimal control problems and simulation of electric circuits. Often this is due to the fact that large scale matrices are suspected to be unsolvable in large scale applications. Since around 2000 efficient low rank theory for matrix equation solvers exists for sparse and also data sparse systems. Unfortunately upto now only incomplete or experimental Matlab implementations of most of these solvers have existed. Here we aim on the implementation of these algorithms in a higher programming language (in our case C) that allows for a high performance solver for many matrix equations arising in the context of large scale standard and generalized state space systems. We especially focus on efficient memory saving data structures and implementation techniques as well as the shared memory parallelization of the underlying algorithms. info:eu-repo/classification/ddc/510 ddc:510 Implementierung Ljapunov-Gleichung Numerische Mathematik Optimale Kontrolle Parallelisierung Systemtheorie Köhler, Martin Saak, Jens Technische Universität Chemnitz 2010-06-11 info:eu-repo/semantics/openAccess doc-type:preprint info:eu-repo/semantics/preprint doc-type:Text https://monarch.qucosa.de/id/qucosa%3A19335 https://monarch.qucosa.de/api/qucosa%3A19335/attachment/ATT-0/ https://monarch.qucosa.de/api/qucosa%3A19335/attachment/ATT-1/ |
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info:eu-repo/classification/ddc/510 ddc:510 Implementierung Ljapunov-Gleichung Numerische Mathematik Optimale Kontrolle Parallelisierung Systemtheorie |
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info:eu-repo/classification/ddc/510 ddc:510 Implementierung Ljapunov-Gleichung Numerische Mathematik Optimale Kontrolle Parallelisierung Systemtheorie Köhler, Martin Saak, Jens Efficiency improving implementation techniques for large scale matrix equation solvers |
description |
We address the important field of large scale matrix based algorithms in control and model order reduction. Many important tools from theory and applications in systems theory have been widely ignored during the recent decades in the context of PDE constraint optimal control problems and simulation of electric circuits. Often this is due to the fact that large scale matrices are suspected to be unsolvable in large scale applications. Since around 2000 efficient low rank theory for matrix equation solvers exists for sparse and also data sparse systems. Unfortunately upto now only incomplete or experimental Matlab implementations of most of these solvers have existed. Here we aim on the implementation of these algorithms in a higher programming language (in our case C) that allows for a high performance solver for many matrix equations arising in the context of large scale standard and generalized state space systems. We especially focus on efficient memory saving data structures and implementation techniques as well as the shared memory parallelization of the underlying algorithms. |
author |
Köhler, Martin Saak, Jens |
author_facet |
Köhler, Martin Saak, Jens |
author_sort |
Köhler, Martin |
title |
Efficiency improving implementation techniques for large scale matrix equation solvers |
title_short |
Efficiency improving implementation techniques for large scale matrix equation solvers |
title_full |
Efficiency improving implementation techniques for large scale matrix equation solvers |
title_fullStr |
Efficiency improving implementation techniques for large scale matrix equation solvers |
title_full_unstemmed |
Efficiency improving implementation techniques for large scale matrix equation solvers |
title_sort |
efficiency improving implementation techniques for large scale matrix equation solvers |
publisher |
Technische Universität Chemnitz |
publishDate |
2010 |
url |
http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000843 https://monarch.qucosa.de/id/qucosa%3A19335 https://monarch.qucosa.de/api/qucosa%3A19335/attachment/ATT-0/ https://monarch.qucosa.de/api/qucosa%3A19335/attachment/ATT-1/ |
work_keys_str_mv |
AT kohlermartin efficiencyimprovingimplementationtechniquesforlargescalematrixequationsolvers AT saakjens efficiencyimprovingimplementationtechniquesforlargescalematrixequationsolvers |
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1719393062759694336 |