14 citations · 39 across the 15 of their papers we have counts for
15 papers
An Exact Algorithm for Computing the Structure of Jordan Blocks
Shinichi Tajima, Katsuyoshi Ohara, Akira Terui
An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing…
Inverse kinematics and path planning of manipulator using real quantifier elimination based on Comprehensive Gröbner Systems
Mizuki Yoshizawa, Akira Terui, Masahiko Mikawa
Methods for inverse kinematics computation and path planning of a three degree-of-freedom (DOF) manipulator using the algorithm for quantifier elimination based on Comprehensive Gr…
Computer-assisted proofs of "Kariya's theorem" with computer algebra
Ayane Ito, Takefumi Kasai, Akira Terui
We demonstrate computer-assisted proofs of "Kariya's theorem," a theorem in elementary geometry, with computer algebra. In the proof of geometry theorem with computer algebra, vert…
Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis
Shinichi Tajima, Katsuyoshi Ohara, Akira Terui
An effective exact method is proposed for computing generalized eigenspaces of a matrix of integers or rational numbers. Keys of our approach are the use of minimal annihilating po…
The GPGCD Algorithm with the Bézout Matrix for Multiple Univariate Polynomials
Boming Chi, Akira Terui
We propose a modification of the GPGCD algorithm, which has been presented in our previous research, for calculating approximate greatest common divisor (GCD) of more than 2 univar…
A Design and an Implementation of an Inverse Kinematics Computation in Robotics Using Real Quantifier Elimination based on Comprehensive Gröbner Systems
Shuto Otaki, Akira Terui, Masahiko Mikawa
The solution and implementation of the inverse kinematics computation of a three degree-of-freedom (DOF) robot manipulator using an algorithm for real quantifier elimination with C…
Solving System of Nonlinear Equations with the Genetic Algorithm and Newton's Method
Ryuji Koshikawa, Akira Terui, Masahiko Mikawa
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses…
Fast Algorithms for Computing Eigenvectors of Matrices via Pseudo Annihilating Polynomials
Shinichi Tajima, Katsuyoshi Ohara, Akira Terui
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials i…
Fast Algorithm for Calculating the Minimal Annihilating Polynomials of Matrices via Pseudo Annihilating Polynomials
Shinichi Tajima, Katsuyoshi Ohara, Akira Terui
Minimal annihilating polynomials are very useful in a wide variety of algorithms in exact linear algebra. A new efficient method is proposed for calculating the minimal annihilatin…
GPGCD: An iterative method for calculating approximate GCD of univariate polynomials
Akira Terui
We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of…
GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials
Akira Terui
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs.…
GPGCD, an Iterative Method for Calculating Approximate GCD of Univariate Polynomials, with the Complex Coefficients
Akira Terui
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to polynomials with the comple…
Recursive Polynomial Remainder Sequence and its Subresultants
Akira Terui
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," along with investigation of their properties. A recursive PRS is defined as,…
Recursive Polynomial Remainder Sequence and the Nested Subresultants
Akira Terui
We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced b…
Subresultants in Recursive Polynomial Remainder Sequence
Akira Terui
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD…