Executable matrix operations on matrices of arbitrary dimensions
We provide the operations of matrix addition, multiplication, trans-position, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (mono-tone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further s...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.656.4278 2023-05-15T14:51:30+02:00 Executable matrix operations on matrices of arbitrary dimensions Christian Sternagel Rene ́ Thiemann The Pennsylvania State University CiteSeerX Archives 2010 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.656.4278 http://afp.sourceforge.net/browser_info/current/AFP/Matrix/outline.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.656.4278 http://afp.sourceforge.net/browser_info/current/AFP/Matrix/outline.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://afp.sourceforge.net/browser_info/current/AFP/Matrix/outline.pdf text 2010 ftciteseerx 2016-01-08T16:38:07Z We provide the operations of matrix addition, multiplication, trans-position, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (mono-tone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic semirings satisfy the axioms that are required by our matrix theory. Our formalization was performed as part of the IsaFoR/CeTA-system [3]1 which contains several termination techniques. The provided the-ories have been essential to formalize matrix-interpretations [1] and arctic interpretations [2]. A short description of this formalization can be found in [4]. Text Arctic Unknown Arctic |
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English |
description |
We provide the operations of matrix addition, multiplication, trans-position, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (mono-tone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic semirings satisfy the axioms that are required by our matrix theory. Our formalization was performed as part of the IsaFoR/CeTA-system [3]1 which contains several termination techniques. The provided the-ories have been essential to formalize matrix-interpretations [1] and arctic interpretations [2]. A short description of this formalization can be found in [4]. |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
Christian Sternagel Rene ́ Thiemann |
spellingShingle |
Christian Sternagel Rene ́ Thiemann Executable matrix operations on matrices of arbitrary dimensions |
author_facet |
Christian Sternagel Rene ́ Thiemann |
author_sort |
Christian Sternagel |
title |
Executable matrix operations on matrices of arbitrary dimensions |
title_short |
Executable matrix operations on matrices of arbitrary dimensions |
title_full |
Executable matrix operations on matrices of arbitrary dimensions |
title_fullStr |
Executable matrix operations on matrices of arbitrary dimensions |
title_full_unstemmed |
Executable matrix operations on matrices of arbitrary dimensions |
title_sort |
executable matrix operations on matrices of arbitrary dimensions |
publishDate |
2010 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.656.4278 http://afp.sourceforge.net/browser_info/current/AFP/Matrix/outline.pdf |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
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Arctic |
op_source |
http://afp.sourceforge.net/browser_info/current/AFP/Matrix/outline.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.656.4278 http://afp.sourceforge.net/browser_info/current/AFP/Matrix/outline.pdf |
op_rights |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
_version_ |
1766322639181185024 |