| Project/Area Number |
09308008
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
計算機科学
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
SASAKI Tateaki Tsukuba Univ., Inst. Math., Professor, 数学系, 教授 (80087436)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Masayuki Iwate Univ., Dept. Inf. Eng., Assoc. Prof., 工学部, 助教授 (20143365)
KAKO Fujio Nara Wo. Univ., Dept. Inf. Sci., Professor, 理学部, 教授 (90152610)
NODA Matu-tarou Ehime Univ., Dept. Comp. Sci., Professor, 工学部, 教授 (10036402)
MOTOYOSHI Fumio Electro-Technical Laboratory, Chief, 知能情報部, 室長
FUKUI Tetsuo Mukogawa Wemen's College, Assoc. Prof., 生活環境学部, 助教授 (70218890)
北本 卓也 筑波大学, 数学系, 助手 (30241780)
|
|---|
| Project Period (FY) |
1997 – 1999
|
| Project Status |
Completed (Fiscal Year 1999)
|
| Budget Amount *help |
¥16,900,000 (Direct Cost: ¥16,900,000)
Fiscal Year 1999: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1998: ¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 1997: ¥9,100,000 (Direct Cost: ¥9,100,000)
|
|---|
| Keywords | approximate algebra / algebraic computation / algebraic-numeric computation / computer algebra / computer algebra system / 数式処理 / 数式処理システム / 近似的代数計算 / 有効浮動少数 / 近似的代数算法 / 有効浮動小数 |
|---|
| Research Abstract |
The purposes of this research are, 1) to develop approximate algebraic algorithms for many algebraic operations, 2) to perform error analysis of approximate algebraic algorithms, 3) to implement the algorithms developed into NSL-GAL system, and 4) to seek for applications of approximate algebra. We performed the following researches for each purpose.
Algorithm study : improvement of approximate factorization algorithm (Sasaki & Nagasaka), theory of Sturm sequence of polynomial with error terms (Sasaki & Terui), decomposition method of multivariate polynomial at a singular point and its application to multivariate factorization (Sasaki & Inaba), rational function interpolation method for bivariate functions (Noda & Kai).
Error analysis : analysis of cancellation errors in multivariate Hensel construction with floating-point numbers (Sasaki & Yamaguchi), analysis of cancellation errors in multivariate resultant computation with floating-point numbers (Sasaki & Sato), evaluation of errors in hybrid rational function approximation based on approximate GCD (Kai & Noda).
Implementation : facilities for approximate algebraic computation in GAL (Kako & Sasaki), a program for calculating polynomial solutions of linear equations with polynomial coefficients (Motoyoshi), development of an interface between GAL and Internet and corresponding modification of GAL (Fukui), a package for computing approximate Grobner basis (Suzuku), a package for computing validated solutions of multivariate polynomial equation by using effective numbers (Suzuki).
Applications : application of algebraic-numeric computation to classification of N lines arrangement on real projective plane (Fukui & Sekiguchi), application of hybrid rational function approximation to singular integral equations appearing in wing theory (Noda & Kai), application of approximate power series solutions of coupled linear equations to algebraic control theory (Kitamoto).
|
