2006年
On perturbation of roots of homogeneous algebraic systems
MATHEMATICS OF COMPUTATION
- ,
- 巻
- 75
- 号
- 255
- 開始ページ
- 1383
- 終了ページ
- 1402
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.1090/S0025-5718-06-01847-3
- 出版者・発行元
- AMER MATHEMATICAL SOC
A problem concerning the perturbation of roots of a system of homogeneous algebraic equations is investigated. The question of conservation and decomposition of a multiple root into simple roots are discussed. The main theorem on the conservation of the number of roots of a deformed (not necessarily homogeneous) algebraic system is proved by making use of a homotopy connecting initial roots of the given system and roots of a perturbed system. Hereby we give an estimate on the size of perturbation that does not affect the number of roots. Further on we state the existence of a slightly deformed system that has the same number of real zeros as the original system in taking the multiplicities into account. We give also a result about the decomposition of multiple real roots into simple real roots.
- リンク情報
- ID情報
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- DOI : 10.1090/S0025-5718-06-01847-3
- ISSN : 0025-5718
- Web of Science ID : WOS:000239181800018