| 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)
|
|---|
| 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).
|
