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Toward high-performance polynomial s...

Li, Xin.

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Toward high-performance polynomial system solvers based on triangular decompositions.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Toward high-performance polynomial system solvers based on triangular decompositions./
作者:	Li, Xin.
面頁冊數:	165 p.
附註:	Source: Dissertation Abstracts International, Volume: 70-08, Section: B, page: 4948.
Contained By:	Dissertation Abstracts International70-08B.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR50246
ISBN:	9780494502464

Toward high-performance polynomial system solvers based on triangular decompositions.
Li, Xin.

Toward high-performance polynomial system solvers based on triangular decompositions. - 165 p.

Source: Dissertation Abstracts International, Volume: 70-08, Section: B, page: 4948.

Thesis (Ph.D.)--The University of Western Ontario (Canada), 2009.

This thesis is devoted to the design and implementation of polynomial system solvers based on symbolic computation. Solving systems of non-linear, algebraic or differential equations, is a fundamental problem in mathematical sciences. It has been studied for centuries and still stimulates many research developments, in particular on the front of high-performance computing.

ISBN: 9780494502464Subjects--Topical Terms:

626642
Computer Science.

Toward high-performance polynomial system solvers based on triangular decompositions.
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520 $a This thesis is devoted to the design and implementation of polynomial system solvers based on symbolic computation. Solving systems of non-linear, algebraic or differential equations, is a fundamental problem in mathematical sciences. It has been studied for centuries and still stimulates many research developments, in particular on the front of high-performance computing.
520 $a Triangular decompositions are a highly promising technique with the potential to produce high-performance polynomial system solvers. This thesis makes several contributions to this effort.
520 $a We propose asymptotically fast algorithms for the core operations on which triangular decompositions rely. Complexity results and comparative implementation show that these new algorithms provide substantial performance improvements.
520 $a We present a fundamental software library for polynomial arithmetic in order to support the implementation of high-performance solvers based on triangular decompositions. We investigate strategies for the integration of this library in high-level programming environments where triangular decompositions are usually implemented.
520 $a We obtain a high performance library combining highly optimized C routines and solving procedures written in the MAPLE computer algebra system. The experimental result shows that our approaches are very effective, since our code often outperforms pre-existing solvers in a significant manner.
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