2013 Fiscal Year Final Research Report
Study of Algorithm and Application of Approximate Groebner Basis
| Project/Area Number |
23500003
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Fundamental theory of informatics
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SAKURAI Tetsuya 筑波大学, システム情報系, 教授 (60187086)
KAKO Fujio 奈良女子大学, 自然科学系, 教授 (90152610)
|
|---|
| Research Collaborator |
INABA Daiju 日本数学検定協会
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | アルゴリズム理論 / 数式処理 / 数値数式融合算法 / 近似グレブナー基底 / 近似特異系と特異化 / 悪条件連立代数方程式 / パラメータ係数線形方程式系 / 疎な線形方程式系 |
|---|
| Research Abstract |
Based on a proposed "approximate ideal", we constructed a theory of approximate Groebner basis, clarified the instability of Buchberger's algorithm on floating point numbbers using a developed subresultnat-like theory, and proposed an algorithm of approximate Groebner basis by stabilizing Buchberger's algorithm.
We also proposed a concept of "approximate singular system" as a multivariate polynomial ideal whose dimension is decreased by a purturbation, and presented an algorithm which recovers the dimension. Applying this operation to algebraic systems of approximately singular type, we proposed a well-conditioning method for such systems. Furthermore, we proposed an error suppressing method and a characteristics extracting method for solving parametric sparse linear systems.
|
