関川 浩（せきがわ ひろし）

東京理科大学 理学部第一部 応用数学科
教授

〒162-8601
東京都 新宿区 神楽坂 1-3
E-Mail: sekigawaXrs.tus.ac.jp (X = @)

最終更新日: 2023年12月27日

現在の研究分野

• 計算代数
• 数式処理
• 数値数式融合計算

略歴

1989.5 - 1991.6: 情報通信処理研究所
LSI の自動設計の研究
1991.7 - 1992.3: 情報通信網研究所
LSI の自動設計の研究
1992.4 - 1994.6: コミュニケーション科学研究所
LSI の自動設計の研究
1994.6 - 1999.1: コミュニケーション科学研究所
計算代数, 数式処理, 数値数式融合計算の研究
1999.1 - 2000.3: コミュニケーション科学基礎研究所
計算代数, 数式処理, 数値数式融合計算の研究

所属学会

• 情報処理学会
• 日本数式処理学会
• 電子情報通信学会
• 日本応用数理学会
• The Association for Computing Machinery (ACM)

最近の文献

• H. Sekigawa, An approximation algorithm for the nearest decomposable polynomial in the Hamming distance, ACM Communications in Computer Algebra, Vol. 57, No. 3, pp. 119-122, 2023.
  DOI: 10.1145/3637529.3637532

• Y. Sato, H. Sekigawa, R. Fukasaku, and K. Nabeshima, On Parametric Border Bases, Mathematical Aspects of Computer and Information Sciences, 8th International Conference (MACIS 2019), Revised Selected Papers, Lecture Notes in Computer Science 11989, pp. 10-15, 2020.
  DOI: 10.1007/978-3-030-43120-4_2

• K. Kondo and H. Sekigawa, Robust computation methods for sparse interpolation of multivariate polynomials, ACM Communications in Computer Algebra, Vol. 53, No. 3, Issue 209, pp. 130-133, 2019.
  DOI: 10.1145/3377006.3377018

• D. Numahata and H. Sekigawa, Robust algorithms for sparse interpolation of multivariate polynomials, ACM Communications in Computer Algebra, Vol. 52, No. 4, Issue 206, pp. 145-147, 2018.
  DOI: 10.1145/3338637.3338648
• Y. Sato, R. Fukasaku, and H. Sekigawa, On Continuity of the Roots of a Parametric Zero Dimensional Multivariate Polynomial Ideal, Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC2018), pp. 359-365, 2018.
  DOI: 10.1145/3208976.3209004

• H. Sekigawa, The Nearest Polynomial to Multiple Given Polynomials with a Given Zero in the Real Case, Theoretical Computer Science, Vol. 681, pp. 167-175, 2017.
  DOI: 10.1016/j.tcs.2017.03.033
• D. Numahata and H. Sekigawa, An algorithm for symbolic-numeric sparse interpolation of multivariate polynomials whose degree bounds are unknown, ACM Communications in Computer Algebra, Vol. 51, No. 1, Issue 199, pp. 18-20, 2017.
  DOI: 10.1145/3096730.3096734

• Y. Kawano and H. Sekigawa, Quantum Fourier Transform over Symmetric Groups---Improved Result, Journal of Symbolic Computation, Vol. 75, pp. 219-243, 2016.
  DOI: 10.1016/j.jsc.2015.11.016

• 関川浩, 複数の多項式に対する最近多項式, 数式処理, Vol. 21, No. 2, pp. 25-28, 2015.

• H. Sekigawa, A Sequence of Nearest Polynomials with Given Factors, Computer Mathematics: 9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012, Contributed Papers and Invited Talks, R. Feng, W-s. Lee, and Y. Sato (Eds.), Springer, pp. 141-145, 2014.
• Y. Kawano and H. Sekigawa, Quantum Fourier transform over symmetric groups--Improved result, ACM Communications in Computer Algebra, Vol. 48, No. 3, Issue 181, pp. 127-129, 2014.
• H. Sekigawa, The Nearest Polynomial to Multiple Given Polynomials with a Given Zero, Proc. 2014 Symposium on Symbolic-Numeric Computation (SNC2014), pp. 144-145, 2014.

• K. Shirayanagi and H. Sekigawa, Interval-symbol method with correct zero rewriting: Reducing exact computations to obtain exact results, Proc. 18th Asian Technology Conference in Mathematics (ATCM2013), pp. 226-235, 2013.
• H. Sekigawa and K. Shirayanagi, Computing a Perturbation Bound for Preserving the Number of Common Zeros of a Polynomial System, Proc. 18th Asian Technology Conference in Mathematics (ATCM2013), pp. 145-154, 2013.
• Y. Kawano and H. Sekigawa, Quantum Fourier Transform over Symmetric Groups, Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC2013), pp. 227-234, 2013.
• 関川浩, 白柳潔, 連立代数方程式の解の個数を保つ摂動限界, 数式処理, Vol. 19, No. 2, pp. 37-40, 2013.

• 白柳潔, 関川浩, 安定化理論に基づく ISCZ 法の凸包構成への応用, 京都大学数理解析研究所講究録 1815“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 133-142, 2012.
• 白柳潔, 関川浩, 安定化理論に基づく ISCZ 法の有効性について, 京都大学数理解析研究所講究録 1814“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 29-35, 2012.
• H. Sekigawa and K. Shirayanagi, Maximal perturbation for preserving the number of solutions of a polynomial system, ACM Communications in Computer Algebra, Vol. 46, No. 3, Issue 181, pp. 120-121, 2012.

• H. Sekigawa, Computing the nearest polynomial with a zero in a given domain by using piecewise rational functions, Journal of Symbolic Computation, Vol. 46, Issue 12, pp. 1318-1335, 2011.
• Y. Kawano and H. Sekigawa, Algorithm for QFT Circuits on Symmetric Groups, Proc. Asian Conference on Quantum Information Science (AQIS2011), pp. 207-208, 2007.
• H. Sekigawa and K. Shirayanagi, Isolated real zero of a real polynomial system under perturbation, ACM Communications in Computer Algebra, Vol. 45, No. 2, Issue 176, pp. 131-132, 2011.
• 関川浩, 白柳潔, 係数に誤差のある連立代数方程式の可解性について, 数式処理, Vol. 17, No. 2, pp. 64-68, 2011.

• H. Sekigawa and K. Shirayanagi, Solvability of bivariate polynomial systems under perturbation, ACM Communications in Computer Algebra, Vol. 44, No. 3, Issue 173, pp. 147-148, 2010.
• Siegfried M. Rump and H. Sekigawa, The ratio between the Toeplitz and the unstructured condition number, Numerical Methods for Structured Matrices and Applications--The Georg Heinig Memorial Volume-- (Operator Theory: Advances and Applications, Vol. 199), Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E., and van Barel, M. (Eds.), Birkhaeuser, pp. 397-419, 2010.

• H. Sekigawa, A Sequence of Nearest Polynomials with Given Factors, Proc. of The Joint Conference of Asian Symposium on Computer Mathematics 2009 (ASCM2009) and International Conference on Mathematical Aspects of Computer and Information Sciences 2009 (MACIS2009), pp. 187-190, 2009.
• 白柳潔, 関川浩, 安定化理論に基づく log method について, 京都大学数理解析研究所講究録 1666“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 98-105, 2009.
• 中山裕貴, 関川浩, 係数に誤差を含む多項式同士の整除性判定, 京都大学数理解析研究所講究録 1666“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 87-97, 2009.
• H. Nakayama and H. Sekigawa, Determining divisibility between polynomials with inexact coefficients, ACM Communications in Computer Algebra, Vol. 43, No. 3, Issue 169, pp. 90-94, 2009.
• K. Shirayanagi and H. Sekigawa, Reducing Exact Computations to Obtain Exact Results Based on Stabilization Techniques, Proc. International Workshop on Symbolic-Numeric Computation 2009 (SNC2009), pp. 191-197, 2009.
• H. Sekigawa, On Real Factors of Real Interval Polynomials, Journal of Symbolic Computation, Vol. 44, Issue 7, pp. 908-922, 2009.
• 白柳潔, 関川浩, 安定化理論に基づく Interval Trace Lifting について, 京都大学数理解析研究所講究録 1652“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 26-32, 2009.
• Y. Nakajima, Y. Kawano, H. Sekigawa, M. Nakanishi, S. Yamashita, and Y. Nakashima, Synthesis of Quantum Circuits for d-level Systems by using Cosine-Sine Decomposition, Quantum Information and Computation, Vol. 9, No. 5&6, pp. 423-443, 2009.
• 関川浩, 数値数式融合計算, 情報処理, Vol. 50, No. 4, pp. 342-348, 2009.

• K. Shirayanagi and H. Sekigawa, A New Groebner Basis Conversion Method Based on the Stabilization Techniques, Theoretical Computer Science, Vol. 409, Issue 2, pp. 311-317, 2008.
• H. Sekigawa, The Nearest Polynomial with a Zero in a Given Domain, Theoretical Computer Science, Vol. 409, Issue 2, pp. 282-291, 2008.
• 関川浩, 与えられた実閉区間に重複零点を持つ最近実多項式, 数式処理, Vol. 15, No. 2, pp. 144-147, 2008.
• H. Sekigawa, The Nearest Real Polynomial with a Real Multiple Zero in a Given Real Interval, Proc. Asian Symposium on Computer Mathematics 2007 (ASCM2007), Lecture Notes in Computer Science 5081, pp. 32-41, 2008.
• H. Sekigawa, The Nearest Polynomial with a Zero in a Given Domain from a Geometrical Viewpoint, Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC2008), pp. 287-294, 2008.
• Y. Nakajima, Y. Kawano, and H. Sekigawa, Efficient Quantum Circuits for Approximating the Jones Polynomial, Quantum Information and Computation, Vol. 8, No. 5, pp. 489-500, 2008.

• H. Sekigawa and K. Shirayanagi, On the Location of Pseudozeros of a Complex Interval Polynomial, Mathematics in Computer Science, Vol. 1, No. 2, pp. 321-335, 2007.
• 白柳潔, 関川浩, 安定化理論に基づくグレブナ基底変換法, 数式処理, Vol. 14, No. 2, pp. 13-17, 2007.
• Y. Nakajima, Y. Kawano, and H. Sekigawa, Synthesis of Quantum Circuits for d-level Systems, Proc. Asian Conference on Quantum Information Science (AQIS2007), pp. 135-136, 2007.
• 白柳潔, 関川浩, 安定化理論における台収束の応用について, 京都大学数理解析研究所講究録 1568“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 20-26, 2007.
• H. Sekigawa, On Real Factors of Real Interval Polynomials, Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC2007), pp. 331-338, 2007.
• P. Khungurn, H. Sekigawa, and K. Shirayanagi, Minimum Converging Precision of the QR-Factorization Algorithm for Real Polynomial GCD, Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC2007), pp. 227-234, 2007.
• H. Sekigawa, The Nearest Polynomial with a Zero in a Given Domain, Proc. International Workshop on Symbolic-Numeric Computation 2007 (SNC2007), pp. 190-196, 2007.
• H. Sekigawa and K. Shirayanagi, On the Location of Zeros of an Interval Polynomial, Symbolic-Numeric Computation (Trends in Mathematics), D. Wang and L. Zhi (eds.), Birkhaeuser, pp. 167-184, 2007.

• 関川浩, 白柳潔, 実区間多項式の実重複零点の所在について, 数式処理, Vol. 13, No. 1, pp. 68-71, 2006.
• 中島裕美, 河野泰人, 関川浩, 量子回路の自動設計手法, 情報処理, Vol. 47, No. 12, pp. 1335-1340, 2006.
• 山本航, 宮本健司, 関川浩, 白柳潔, 円に関する人間らしい初等幾何証明を生成するための推論方法, 京都大学数理解析研究所講究録 1514“Computer Algebra---Design of Algorithms, Implementations and Applications,” pp. 164-170, 2006.
• T. Moriya, N. Harada, Y. Kamamoto, and H. Sekigawa, MPEG-4 ALS--International Standard for Lossless Audio Coding, NTT Technical Review, Vol. 4, No. 8, pp. 40-45, 2006.
• H. Sekigawa and K. Shirayanagi, Locating Real Multiple Zeros of a Real Interval Polynomial, Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC2006), pp. 310-317, 2006.
• K. Miyamoto, W. Yamamoto, H. Sekigawa, and K. Shirayanagi, Deductive System for Human-like Proofs in Geometry, Proc. 13th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning 2006 (Calculemus'06), pp. 5-20, 2006.
• 関川 浩, 白柳 潔, 区間多項式の零点の所在について, 電子情報通信学会論文誌分冊A, Vol. J89-A, No. 3, pp. 199-216, 2006.
• 原田登, 守谷健弘, 関川浩, 白柳潔, 鎌本優, ISO/IEC MPEG-4 Audio Lossless Coding (ALS) における IEEE754 浮動小数点時系列信号の可逆符号化, 電子情報通信学会論文誌分冊B, Vol. J89-B, No. 2, pp. 204-213, 2006.
• Y. Nakajima, Y. Kawano, and H. Sekigawa, A New Algorithm for Producing Quantum Circuits using KAK Decompositions, Quantum Information and Computation, Vol. 6, No. 1, pp. 67-80, 2006.

• 関川浩, 白柳潔, 実区間多項式の零点の所在について, 数式処理, Vol. 12, No. 2, pp. 35-38, 2005.
• H. Sekigawa and K. Shirayanagi, On the Location of Pseudozeros of a Complex Interval Polynomial, Proc. Asian Symposium on Computer Mathematics 2005 (ASCM2005), pp. 231-234, 2005.
• 白柳潔, 宮本健司, 山本航, 関川浩, 人間らしい初等幾何証明における角の取り扱いについて, 京都大学数理解析研究所講究録 1456, "Computer Algebra--Design of Algorithms, Implementations and Applications," pp. 90-99, 2005.
• H. Nakajima, Y. Kawano, H. Sekigawa, An Algorithm for Decomposing Unitary Matrices using Cartan Decomposition, Abstracts of 11th International Conference on Applications of Computer Algebra (ACA'2005), p. 24, 2005.
• H. Sekigawa and K. Shirayanagi, On the Location of Zeros of a Complex Interval Polynomial, Abstracts of 11th International Conference on Applications of Computer Algebra (ACA'2005), p. 15, 2005.
• H. Sekigawa and K. Shirayanagi, On the Location of Zeros of an Interval Polynomial, Proc. International Workshop on Symbolic-Numeric Computation 2005 (SNC2005), pp. 144-165, 2005.
• 河野泰人, 木村欣司, 関川浩, 野呂正行, 白柳潔, スピンの交換だけを用いた量子コンピュータにおける厳密な CNOT の存在, 数式処理, Vol. 11, No. 2, pp. 55-58, 2005.
• Y. Kawano, K. Kimura, H. Sekigawa, M. Noro, K. Shirayanagi, M. Kitagawa, and M. Ozawa, Existence of the Exact CNOT on a Quantum Computer with the Exchange Interaction, Quantum Information Processing, Vol. 4, No. 2, pp. 65-85, 2005.
• N. Harada, T. Moriya, H. Sekigawa, and K. Shirayanagi, Lossless Compression of IEEE Floating-point Audio using Approximate Common Factor Coding and Masked-LZ Compression, Poster presentation at AES 118th Convention, 2005.

• 関川 浩, 近似計算を用いた代数的数のゼロ判定法, 応用数理, Vol. 14, No. 4, pp. 75-78, 2004.
• 宮本健司, 大矢孝次, 関川 浩, 白柳 潔, 初等幾何の自動証明における効率的な補助線の発見法について, 京都大学数理解析研究所講究録 1395, "Computer Algebra--Design of Algorithms, Implementations and Applications," pp. 157-163, 2004.
• 河野泰人, 木村欣司, 関川 浩, Decoherence-free Subspace における量子ゲートについて, 信学会 コンピュテーション研究会 電子情報通信学会技術研究報告, COMP2004-23, pp. 33-39, 2004.

• 宮本健司, 関川 浩, 白柳 潔, 町田文彦, 初等幾何における読みやすい証明の生成手法について, 京都大学数理解析研究所講究録 1335, "Computer Algebra--Algorithms, Implementations and Applications," pp. 20-27, 2003.

• 白柳 潔, 関川 浩, 新しい科学技術計算方式--数値計算と数式処理の融合, NTT R&D, Vol. 51, No. 10, pp. 778-783, 2002.

• H. Sekigawa, A Remark on the Polynomial Determining Superstable Points in the Mandelbrot Set, Josai Mathematical Monographs 2, NLA99 Computer Algebra, pp. 11-13, 2000.
• H. Sekigawa and K. Shirayanagi, Automatic Algorithm Stabilization System, Josai Mathematical Monographs 2, NLA99 Computer Algebra, pp. 159-168, 2000.

• H. Sekigawa and K. Koyama, Nonexistence Conditions of a Solution for the Congruence x₁^k+...+x_s^k=N (mod pⁿ), Mathematics of Computation, Vol. 68, No. 227, pp. 1283-1297, 1999.

• H. Sekigawa, Using Interval Computation with the Mahler Measure for Zero Determination of Algebraic Numbers, 城西情報科学研究, Vol. 9, No. 1, pp. 83-99, 1998.

• 白柳 潔, 関川 浩, ゼロ書き換えに基づいた区間法とSturmのアルゴリズムへの応用, 電子情報通信学会論文誌分冊A, Vol. J80-A, No. 5, pp. 791-802, 1997.
• K. Koyama, Y. Tsuruoka, and H. Sekigawa, On Searching for Solutions of the Diophantine Equation x³+y³+z³=n, Mathematics of Computation, Vol. 66, No. 218, pp. 841-851, 1997.

• H. Sekigawa, Using Interval Arithmetic and Polynomial Norms to Determine Signs of Algebraic Numbers, Proc. 2nd Asian Symposium on Computer Mathematics (ASCM'96), pp. 43-53, 1996.
• H. Sekigawa, An Interval Arithmetic with Algebraic Complexity to Determine the Signs of Algebraic Expressions, Abstracts of 4th International Symposium on Effective Methods in Algebraic Geometry (MEGA'96), p. 43, 1996.

• H. Sekigawa and K. Shirayanagi, Computing Diophantine Approximate Groebner Bases, Proc. 1st Asian Technology Conference in Mathematics (ATCM'95), pp. 717-726, 1995.
• H. Sekigawa and K. Shirayanagi, Zero Rewriting in Interval Computation and Its Application to Sturm's Algorithm, Poster presentation at International Symposium on Symbolic and Algebraic Computation (ISSAC'95).