Using symmetries in the eigenvalue method for polynomial systems

被引：6

作者：

Corless, Robert M. ^{[1
]}

Gatermann, Karin ^{[2
]}

Kotsireas, Ilias S. ^{[3
]}

机构：

[1] Univ Western Ontario, Dept Appl Math, Ontario Res Ctr Comp Algebra, London, ON N6A 5B7, Canada

[2] Univ Western Ontario, Dept Comp Sci, London, ON N6A 5B7, Canada

[3] Wilfrid Laurier Univ, Dept Phys & Comp Sci, Waterloo, ON N2L 3C5, Canada

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2009年 / 44卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

GROBNER BASES; SAGBI-BASES;

D O I：

10.1016/j.jsc.2008.11.009

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

One way of solving polynomial systems of equations is by computing a Grobner basis, setting up an eigenvalue problem and then computing the eigenvalues numerically. This so-called eigenvalue method is an excellent bridge between symbolic and numeric computation, enabling the solution of larger systems than with purely symbolic methods. We investigate the case that the system of polynomial equations has symmetries. For systems with symmetry, some matrices in the eigenvalue method turn out to have special structure. The exploitation of this special structure is the aim of this paper. For theoretical development we make use of SAGBI bases of invariant rings. Examples from applications illustrate our new approach. (C) 2009 Published by Elsevier Ltd

引用

页码：1536 / 1550

页数：15

共 50 条

[41] Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem
Wei, Wei
Dai, Hua
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2018, 8 (01) : 82 - 99
[42] A new method for singular polynomial systems
Sang, Haifeng
Liu, Panpan
Li, Qingchun
Li, Yan
Communications in Computer and Information Science, 2014, 472 : 357 - 363
[43] A New Method for Singular Polynomial Systems
Sang, Haifeng
Liu, Panpan
Li, Qingchun
Li, Yan
BIO-INSPIRED COMPUTING - THEORIES AND APPLICATIONS, BIC-TA 2014, 2014, 472 : 357 - 363
[44] Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion-Application to a Finite Element Rotor
Sarrouy, E.
Dessombz, O.
Sinou, J. -J.
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2012, 134 (05):
[45] LINEAR MECHANICAL BOUNDARY - EIGENVALUE PROBLEMS WITH SYMMETRIES
NANNI, J
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1977, 28 (03): : 493 - 512
[46] NUMERICAL TREATMENT OF NATURAL EIGENVALUE PROBLEMS OF 4TH ORDER USING COLLOCATION METHOD WITH LAGRANGE POLYNOMIAL THEOREM
BROCKS, W
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1972, 23 (06): : 870 - 880
[47] Linearizations of polynomial matrices with symmetries and their applications
Antoniou, E
Vologianndis, S
Karampetakis, N
2005 IEEE INTERNATIONAL SYMPOSIUM ON INTELLIGENT CONTROL & 13TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION, VOLS 1 AND 2, 2005, : 159 - 163
[48] Detecting symmetries in polynomial Bezier curves
Sanchez-Reyes, J.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 288 : 274 - 283
[49] Stabilization of nonaffine systems: A constructive method for polynomial systems
Moulay, E
Perruquetti, W
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (04) : 520 - 526
[50] Linearizations of polynomial matrices with symmetries and their applications
Antoniou, EN
Vologiannidis, S
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2006, 15

← 1 2 3 4 5 →