| KONDO Koichi | |
| Faculty of Science and Engineering Department of Electrical Engineering | |
| Professor |
Last Updated :2025/05/07
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博士（工学）．愛知県尾張旭市生まれ．同志社大学大学院博士課程（前期課程）修了．大阪大学大学院博士（後期課程）退学．専門は，応用数学，ソリトン理論，数値解析．所属学会は，日本応用数理学会．国内特許１件．
Research Interests
- 多倍長精度演算
- ニュートン法
- 数値計算
- 固有値
- 固有値問題
- Discrete Integrable System
- Integrable System
- Applied Mathematics
- Inverse Eigenvalue Problem
- Numerical Analysis
- Chaos
- Discrete Dynamical System
- Soliton
- discrete dynamical systems
Research Areas
Research Experience
- Doshisha University, Graduate School of Science and Engineering, 博士後期課程 教授, 2018/04 - Today
- Doshisha University, Graduate School of Science and Engineering, 博士前期課程 教授, 2015/04 - Today
- Doshisha University, Faculty of Science and Engineering, Department of Electrical Engineering, 教授, 2015/04 - Today
- Doshisha University, Graduate School of Science and Engineering, 博士前期課程 准教授, 2012/04 - 2015/03
- Doshisha University, Faculty of Science and Engineering, Department of Electrical Engineering, 准教授, 2010/04 - 2015/03
- Doshisha University, 大学院工学研究科, 博士前期課程 准教授, 2010/04 - 2012/03
- Doshisha University, 工学部電気工学科, 専任講師, 2002/04 - 2008/03
- Lecturer, Department of Electrical Engineering, Faculty of Engineering, Doshisha University, 2002 - 2008
- - Associate Professor, Department of Electrical Engineering, Faculty of Science and Engineering, Doshisha University, 2008 -
- Osaka University, Graduate School of Engineering Science, 助手, 1999/04 - 2002/03
- Research Asistant, Graduate School of Engineering Science, Osaka Univiersity, 1999 - 2002
Education
- Osaka University, 基礎工学研究科, 数理科学分野, 1997/04 - 1999/03
- Osaka University, Graduate School, Division of Engineering Science, - 1999
- Doshisha University, 工学研究科, 電気工学専攻, 1995/04 - 1997/03
- Doshisha University, Graduate School, Division of Engineering, - 1997
- Doshisha University, 工学部, 電子工学科, 1992/04 - 1995/03
- Doshisha University, Faculty of Engineering, - 1995
Degree
Association Memberships
Published Papers
- Discrete hungry integrable systems — 40 years from the Physica D paper by W. W. Symes
Masato Shinjo; Akiko Fukuda; Koichi Kondo; Yusaku Yamamoto; Emiko Ishiwata; Masashi Iwasaki; Yoshimasa Nakamura
Physica D: Nonlinear Phenomena, Elsevier BV, 439 133422 - 133422, Nov. 2022, Scientific journal - The Kostant-Toda equation and the hungry integrable systems
Masato Shinjo; Masashi Iwasaki; Koichi Kondo
J. Math. Anal. Appl., 483(123627) 1 - 15, Mar. 2020, Scientific journal - 一般の行列に関するラックス系（LU型，コレスキー型，QR型）の離散化について
中澤 朋亮; 近藤 弘一
九州大学応用力学研究所研究集会報告, 2019AO-S2(17) 95 - 101, Mar. 2020 - 離散戸田方程式を用いた要素および固有値が指定された逆固有値問題の解法
赤岩香苗; 谷口雄大; 近藤弘一
九州大学応用力学研究所研究集会報告, 29AO-S7(1) 101 - 106, Mar. 2018, Research institution - An arbitrary band structure construction of totally nonnegative matrices with prescribed eigenvalues
Kanae Akaiwa; Yoshimasa Nakamura; Masashi Iwasaki; Akira Yoshida; Koichi Kondo
NUMERICAL ALGORITHMS, SPRINGER, 75(4) 1079 - 1101, Aug. 2017, Scientific journal - A finite-step construction of totally nonnegative matrices with specified eigenvalues
Kanae Akaiwa; Yoshimasa Nakamura; Masashi Iwasaki; Hisayoshi Tsutsumi; Koichi Kondo
NUMERICAL ALGORITHMS, SPRINGER, 70(3) 469 - 484, Nov. 2015, Scientific journal - A tridiagonal matrix construction by the quotient difference recursion formula in the case of multiple eigenvalues
Kanae Akaiwa; Masashi Iwasaki; Koichi Kondo; Yoshimasa Nakamura
Pacific Journal of Mathematics for Industry, Institute of Mathematics for Industry, Kyushu University ; c2014-, 6(10) 1 - 9, Nov. 2014, Scientific journal - Numerical performance of hyperplane constrained method and its hybrid method for singular value decomposition
Kenichi Yadani; Koichi Kondo; Masashi Iwasaki
COMPUTING, SPRINGER WIEN, 92(3) 265 - 283, Jul. 2011, Scientific journal - Solutions of Sakaki-Kakei equations of type 1, 2, 7 and 12
Koichi Kondo
JSIAM Letters, The Japan Society for Industrial and Applied Mathematics, 3 45 - 48, Jul. 2011, Scientific journal - Solutions of Sakaki-Kakei equations of type 3, 5 and 6
Koichi Kondo
JSIAM Letters, The Japan Society for Industrial and Applied Mathematics, 2 73 - 76, Jul. 2010, Scientific journal - A singular value decomposition algorithm based on solving hyperplane constrained nonlinear systems
Kenichi Yadani; Koichi Kondo; Masashi Iwasaki
APPLIED MATHEMATICS AND COMPUTATION, ELSEVIER SCIENCE INC, 216(3) 779 - 790, Apr. 2010, Scientific journal - On the convergence of the V-type hyperplane constrained method for singular value decomposition
Kenichi Yadani; Koichi Kondo; Masashi Iwasaki
JSIAM Letters, The Japan Society for Industrial and Applied Mathematics, 2 21 - 24, Apr. 2010, Scientific journal - Mixed double-multiple precision version of hyperplane constrained method for singular value decomposition
Kenichi Yadani; Koichi Kondo; Masashi Iwasaki
JSIAM Letters, The Japan Society for Industrial and Applied Mathematics, 2 25 - 28, Apr. 2010, Scientific journal - On a Max-Plus Version of the Stieltjes Function
Atsushi Mukaihira; Yuya Mori; Koichi Kondo
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, AMER INST PHYSICS, 1281 2099 - 2102, 2010, International conference proceedings - Eigendecomposition algorithms solving sequentially quadratic systems by Newton method
Koichi Kondo; Shinji Yasukouchi; Masashi Iwasaki
JSIAM Letters, The Japan Society for Industrial and Applied Mathematics, 1 40 - 43, Jul. 2009, Scientific journal - An SVD algorithm based on solving nonlinear systems
Kondo Koichi; Sugimoto Shohei; Iwasaki Masashi
Transactions of the Japan Society for Industrial and Applied Mathematics, The Japan Society for Industrial and Applied Mathematics, 19(1) 81 - 103, Mar. 2009, Scientific journal - Kakarala-Ogunbona の画像分解における特異値の近接度を低減するアルゴリズム
近藤弘一; 笹田昇平; 小幡雅彦; 岩崎雅史; 中村佳正
情報処理学会論文誌：コンピューティングシステム, 48(SIG8) 216 - 225, May 2007, Scientific journal - 教育用計算機システムにおけるプリンタシステムに求められる要求とその実装
桝田秀夫; 小川剛史; 齊藤明紀; 中村匡秀; 近藤弘一; 中西通雄
情報処理学会論文誌, 46, 2005, Scientific journal - Determinantal solutions of solvable chaotic systems
K Kondo; Y Nakamura
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 145(2) 361 - 372, Aug. 2002, Scientific journal - Studies on Integrability for Nonlinear Dynamical Systems and its Applications
Koichi Kondo
大阪大学, Jun. 2001, Doctoral thesis - An extension of the Steffensen iteration and its computational complexity
Koichi Kondo; Yoshimasa Nakamura
Interdisciplinary Information Sciences, Tohoku University, 4(1) 129 - 138, 1998, Scientific journal - Solution and integrability of a generalized derivative nonlinear Schrodinger equation
K Kondo; K Kajiwara; K Matsui
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 66(1) 60 - 66, Jan. 1997, Scientific journal
MISC
- 固有値分解のための超平面制約法に対する理論解析
吉武奈緒美; 岩崎雅史; 近藤弘一
九州大学応用力学研究所研究集会報告, 22AO-S8 214 - 219, Mar. 2011, Report research institution - ２次非線形方程式系の解法に基づく行列の対角化法
近藤弘一; 杉本昌平; 岩崎雅史
京都大学数理解析研究所講究録, 京都大学, 1614 156 - 165, Oct. 2008, Report scientific journal - 特異値分解を用いた画像圧縮方法に関する研究
笹田昇平; 近藤弘一; 岩崎雅史
九州大学応用力学研究所研究集会報告, 19ME-S2 167 - 172, Apr. 2008, Report research institution - 微分積分学における和歌山大学と同志社大学の実践例について
川上智博; 長瀬照子; 森淳秀; 近藤弘一
和歌山大学教育学部教育実践総合センター紀要, 17 75 - 80, Aug. 2007, Report research institution - Bスプラインガラーキン法による数値シミュレーション
杉本昌平; 近藤弘一
九州大学応用力学研究所研究集会報告, 18ME-S5(Article No. 28) 1 - 10, May 2007, Report research institution - 特異値分解を用いた画像分解における特異値クラスタを緩和するアルゴリズム
笹田昇平; 近藤弘一; 岩崎雅史; 中村佳正
九州大学応用力学研究所研究集会報告, 18ME-S5(Article No. 27) 1 - 10, May 2007, Report research institution - ウェーブレット級数展開に基づく数値シミュレーション
山口貴史; 近藤弘一
九州大学応用力学研究所研究集会報告, 17ME-S2(Article No. 35) 1 - 6, May 2006, Report research institution - 画像圧縮に適した特異値分解アルゴリズムの考察
小幡雅彦; 岩崎雅史; 近藤弘一; 守本晃; 芦野隆一; 中村佳正
情報処理学会研究報告（HPC, ARC）, 2006 169 - 174, Feb. 2006, Report research institution - On a Singular Value Algorithm Suited to Image Compression
2006 169 - 174, 2006 - 熱音響冷却システムにおける作業流体とスタック間の熱交換についての数理モデル
富樫萌子; 坂本真一; 近藤弘一
九州大学応用力学研究所研究集会報告, 16ME-S1 204 - 209, Apr. 2005, Report research institution - Beylkin法によるウェーブレット変換を用いた数値シミュレーション
宮川昌也; 近藤弘一
九州大学応用力学研究所研究集会報告, 15ME-S3 233 - 238, Apr. 2004, Report research institution - 離散方程式の分子解と直交多項式
辻本諭; 近藤弘一
京都大学数理解析研究所講究録, 京都大学, 1170 1 - 8, Sep. 2000, Report research institution - ニュートン法と可解カオスの行列式解
近藤弘一; 中村佳正
九州大学応用力学研究所研究集会報告, 11ME-S4 53 - 58, Mar. 2000, Report research institution - 高次収束する Steffensen 型反復解法
近藤弘一; 中村佳正
京都大学数理解析研究所講究録, 京都大学, 1040 228 - 236, Apr. 1998, Report research institution - ニュートン・ステファンセン・シャンクス
近藤弘一; 中村佳正
京都大学数理解析研究所講究録, 京都大学, 1020 28 - 38, Dec. 1997, Report research institution - Solution and integrability of a generalized derivative nonlinear Schrodinger equation
K Kondo; K Kajiwara; K Matsui
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 66(1) 60 - 66, Jan. 1997 - Solution and integrability of a generalized derivative nonlinear Schrödinger equationSolution and integrability of a generalized derivative nonlinear Schrödinger equation
Koichi Kondo
J. Phy. Soc. Japan, 66 60 - 66, 1977
Industrial Property Rights
Research Projects
- New developments of matrix similarity transformations derived from integrable systems
Iwasaki Masashi; YAMAMOTO Yusaku; ISHIWATA Emiko; KONDO Koichi; FUKUDA Akiko; SHINJO Masato
One of the results is to improve the I-SVD algorithm for computing singular value decompositions of bidiagonal matrices with higher accuracy. The new I-SVD algorithm employs the proposed dLVs algorithm for singular values and the proposed divided Twisted factorization method for singular vectors. The second is to investigate the convergence of solutions to dynamical systems to eigenvalues of various band matrices. Solution expressions of the discrete hungry integrable systems and their asymptotic convergence are thoroughly clarified. A new algorithm for computing eigenvalues of pentadiagonal matrices is also designed. The third is to find relationships among the discrete hungry integrable systems, extended Fibonacci sequences and roots of polynomials, and then develop them in constructing band matrices with prescribed eigenvalues. New characteristic polynomials of matrices are also presented over min-plus algebra., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2014/04 -2017/03, Grant-in-Aid for Scientific Research (C), Kyoto Prefectural University - Studies on matrix diagonalization by solving nonlinear systems
KONDO Koichi
The matrix diagonalizations, for example eigenvalue decomposition, singular value decomposition, are basic topics in linear algebra, and they also important tools in various fields. In this research, we developed new method, which is called the hyperplane-constrained method. This method can obtain matrix diagonalization by solving the nonlinear systems, which are constrained on hyperplanes, by the Newton method. The problems on selecting initial vectors of the Newton method is avoided by suitable selecting the normal vectors of the hyperplanes., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2008/04 -2012/03, Competitive research funding, Grant-in-Aid for Young Scientists (B), Doshisha University - Research for new algorithms by integrable system approach
IWASAKI Masashi; KONDO Koichi; ISHIWATA Emiko; YAMAMOTO Yusaku; NAKAMURA Yoshimasa
We design new three kinds of algorithms based on the studies of integrable systems. One of our proposal algorithms is matrix eigenvalues algorithm for band matrices. The second is matrix diagonalization algorithm for general matrices. The third is matrix eigenvalues algorithm in Max-Plus algebra. We also clarify some numerical properties of our proposal algorithms and existing algorithms., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2008 -2010, Grant-in-Aid for Young Scientists (B), Kyoto Prefectural University - Verification of the efficiency of the Grobner Basis for Various Combinatorial Problems
KONDO Koichi
1) 最尤復号の問題に付随する格子イデアルについて調べ, 符号が完全符号のときは, 復号に必要なイデアルの次数順序に関するグレブナー基底が, 最小重みの符号語だけで完全に決まることを示した. 2) 最大流問題を整数計画問題として定式化し, 最大流問題に付随する整数計画問題の係数行列は縮小接続行列のローレンス持ち上げとして得られることから, 最大流問題に付随するトーリックイデアルの普遍グレブナー基底が, 有向グラフにおい辺の向きを無視した閉路に対応する2項式と辺の向きを無視した始点から終点への路に対応する2項式全体の和集合からなることを示した., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2006 -2008, Grant-in-Aid for Scientific Research (C), Doshisha University - On diagonalization of matrix by solving nonlinear systems
2008, Competitive research funding - ソリトン理論に基づく非線形離散力学系に関する可積分系条件の探求
近藤 弘一
可積分系アルゴリズムを用いた数値計算アルゴリズムの開発およびその応用を行う. Kakarara-Ogunbonaによる特異値分解を用いた画像圧縮アルゴリズムに関する研究では,特異値の近接度を緩和するアルゴリズムを考案した.ある特殊な画像に対しては特異値が近接し多くの数値誤差を含む可能性がある.これを回避するため画像にある縁取りを施すことで近接度を緩和し,数値不安定性を回避することに成功した.この研究成果を特許出願した.また,ウェーブレット変換による数値シミュレーションでは,各種基底と時間差分スキームと組み合わせによる数値誤差を評価し,次の研究発表を行う. 学術論文誌 ●近藤弘一,笹田昇平,小幡雅彦,岩崎雅彦,中村佳正:Kakarala-Ogunbonaの画像分解における特異値の近接度を低減するアルゴリズム,情報処理学会論文誌:コンピューティングシステムACS18,2007. 学会発表 ・ Shohei SUGIMOTO, Shohei SASADA, and Koichi KONDO : Numerical simulations for evolutionary PDEs by the wavelet-Galerkin method, SIAM Conference on Nonlinear Waves and Coherent Structures 2006, University of Washington, September 10, 2006. ●笹田昇平,近藤弘一,岩崎雅史,中村佳正:特異値分解による画像分割で現れる特異値の近接度を緩和する方法,日本応用数理学会年会,筑波大学,2006年9月16日. 研究集会発表 ●笹田昇平,近藤弘一,岩崎雅史,中村佳正:特異値分解を用いた画像分解における特異値クラスタを緩和するアルゴリズム,研究集会「非線形波動現象における基礎理論数値計算および実験のクロスオーバー」,九州大学応用力学研究所,2006年11月7. ●杉本昌平,近藤弘一:Bスプラインガラーキン法による数値シミュレーション,研究集会「非線形波動現象における基礎理論,数値計算および実験のクロスオーバー」,九州大学応用力学研究所,2006年11月7日., 日本学術振興会, 科学研究費助成事業, 2004 -2006, 若手研究(B), 同志社大学 - Study of the integrable systems in mathematical physics and applied analysis
OHMIYA Mayumi; WATANABE Yoshihide; KONDO Koichi
We clarified the isomonodromic property of the Darboux-Lame equation obtained by the double Darboux transformation for the 2^Lame equation. Using this, we succeeded to characterize the differential equations of Heun type whose monodromy can be exactly calculable by transforming it to the differential equation on the complex projective line by a covering map. Moreover, applying the classical Appell's lemma, we developed a new algorithm of solving the differential equations. In addition, we extended the spectral degenerate condition of Darboux transformation to the non-spectral case. Furthermore, we investigated the asymptotic behavior of the elliptic multi-soliton solutions applying this result, and discovered the new addition formula of the elliptic function. On the other hand, we accomplished the study of the modulation instability of the strongly dispersive nonlinear system, and decided the modulation instability zone of the wave numbers of the nonhomoclinic solution to Sine-Gordon equation. At the same time, we carried out the numerical study of such unstable phenomena using Hirota's difference scheme, and showed that this scheme was fairly useful even for the unstable phenomena. On the one hand, we proved the iso-spectral property of the double Darboux transformation, and clarified the equivalence of the iso-monodromic property and the iso-spectral property in some specific case. Moreover, we studied the formula for the reconstruction of qubit density matrix in NMR quantum computing. Moreover, we studied the GHZ state of 5 qubits NMR quantum computing. On the other hand, we studied the application of Grobner basis. In particular, we implemented the computation of Grobner basis of the toric ideal to the computer algebra system "Asir". We studied the application of the wavelet analysis to the numerical analysis of the nonlinear wave motion, and verified certain efficiency of Beylkin's method. On the other hand, we constructed the mathematical model of the heat acoustic cooling system as nonlinear phenomena. Moreover, we studied the appropriate singular value decomposition algorithm for the image compression applying the wavelet analysis., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2003 -2005, Grant-in-Aid for Scientific Research (C), Doshisha University - Research on algebraic structures of ultradiscrete soliton equations and applications to engineering
NAGAI Atsushi; KONDO Koichi; TSUJIMOTO Satoshi; OKADO Masato
The purpose of this research is to find algebraic and analytical structures of differential, difference and ultradiscrete equations, and to apply, the mathematical results to the field of engineering. The main results obtained are as follows. 1. We have found conserved quantities of box and ball systems with arbitrary box capacities by making use of ultradiscrete KdV and Lotka-Volterra equation including their modified version. 2. We have obtained piecewise linear equation of combinatorial R of crystals associated with D type affine Lie algebra by employing inverse ultra-discretization. 3. A discrete integrable system called the RI chain, which is considered as a generalization of the Toda equation, is studied. In particular, we have obtained its bilinear form and its determinant solution. The relation with relativistic Toda equation is also found. 4. We have obtained discrete and q-discrete versions of fractional derivative together with ite eigen function called the Mittag-Leffler function. We have also constructed a new integrable mapping with fractional difference. 5. We have found Green and Poisson functions for a biharmonic operator on a disk. Their integral representations are also found., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2001 -2003, Grant-in-Aid for Scientific Research (C), Osaka University - Continued fraction expansions in terms of discrete integrable systems and their applications to systems identifications and the BCH-Goppa decoding
NAKAMURA Yoshimasa; IMAI Jun; NAKAYAMA Isao; SHIROTA Norihisa; KONDO Koichi; OKAZAKI Ryotaro
There has not been known a continued fraction expansion of order O(N^2) for the Perron continued fraction, which emerges in the Carathe\'odory interpolation problem, such as the qd algorithm for the Chebyshev continued fraction. First Nakamura and coworkers, being based on the orthogonal polynomials on the unit circle, derived a new integrable system named the Schur flow which has a Lax representation given by the three terms recurrence relation. Secondly in terms of the discrete Schur flow they designed a new continued fraction expansion algorithm of order O(N^2) for the Perron continued fraction and its application to algorithm for computing zeros of certain algebraic equations. Consequently, the new correspondence 1)classical orthogonal polynomials -Chebyshev continued fraction -Toda equation 2)orthogonal polynomials on the unit circle -Perron continued fraction -Schur flow is revealed. They also considered the Thron continued fraction through the relativistic Toda equation having a Lax representation given by the three terms recurrence relation for the bi-orthogonal polynomials. An integrable discretization of the equation enable them to design a new continued fraction algorithm of order O(N^3) for the Thron fraction. This algorithm has an advantage that it computes the continued fraction for the case where the FG algorithm does not work. Nakamura showed that a Pad\'e approximation, namely, a continued fraction expansion of the Laplace transform of the Airy function can be computed in a pure algebraic manner. Each coefficients of the continued fraction is connected by the By\"acklund transformation of the second Painlev\'e equation PII, where one of the Lax pair is just the recurrence relation of orthogonal polynomials., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2000 -2003, Grant-in-Aid for Scientific Research (B) - 非線形力学系に関する可積分条件の探求とその応用
1999/04 -2002/03, Competitive research funding - Study on Formal Integrability of Systems of Evolution Equations
WATANABE Yoshihide; KONDO Koichi; KAJIWARA Kenji; OHMIYA Mayumi
・ We enumerate systems of evolution equations formally completely integrable in the sense of Sokolov and Shabat, that is, equations admitting strong symmetries and strong conservation laws. The calculation is performed with the computer algebra system REDUCE and under the two assumptions : (1) Time evolution is described by polynomials of dependent variables and their derivatives with respect to the spatial variable x, and such polynomials are homogeneous with respect to a suitable weight for the derivation. (2) Time evolution is linear with constant coefficients with respect to the highest order spatial derivative. We enumerate systems of 4-th order equations and get the list for the weight 1. ・ The Gelfand-Dickey transformation transforms differential polynomials into symmetric polynomials, then the problem of finding the kernel of the Euler operator is reduced to the problem of finding invariants of the finite group called the Euler group, We have implemented the algorithm by Sturmfels which calculates generating invariants of finite groups to the computer algebra system Asir. ・ We have calculated the monodromy group for the second order Darboux-Lame equation and established the method for calculating the position of singularities for such potentials. ・ A birational realization of Affine-Weyl group A^<(1)>_× A^<(1)>_ is given, and in terms of this representation, some discrete integrable systems are constructed. We also derived a hierarchy of discrete dynamical systems which admit the above affine-Weyl group as the symmetry group and proved that the hierarchy is obtained from the q-KP hierarchy by reduction. ・ It is shown that two solvable chaotic systems, the arithmetic-harmonic mean (AHM) algorithm and the Ulam-von Neuman (UvN) map, admit determinantal solutions., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2001 -2002, Grant-in-Aid for Scientific Research (C), DOSHISHA UNIVERSITY - Studies on the orthogonal polynomials, the continued fractions and the discrete integrable systems
TSUJIMOTO Satoshi; KONDO Koichi; NAGAI Atsushi; NAKAMURA Yoshimasa
In the last decades, discrete integrable system has been getting a lot of attention from the viewpoints of difference scheme and algorithm. Already there have been many discussions about relations between continuous-time integrable system and orthogonal polynomials. There are only a few studies on the relations between full-discretised (discrete time and space) systems and orthogonal polynomials fully clarified, such as the discrete integrable system (Toda, Lotka-Volterra) and classical orthogonal polynomials by Spiridonov and Zhedanov. Hence the purpose of this studies is to clarify the relations between the discrete integrable system and the orthogonal polynomials and to develop the Numerical algorithms related to the orthogonality. At first, we pick up the discrete hungry Lotka-Volterra equation and the coupled KP equation. We probe them by means of Hirota's tau-function and develop the relations., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2000 -2001, Grant-in-Aid for Scientific Research (C) - Studies on integrability for nonlinear dynamical systems and its applications
1999, Competitive research funding