Hiroshi Sekigawa

Associate Professor
Department of Mathematics, School of Science, Tokai University
4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292 Japan
E-mail: sekigawaXtokai-u.jp (X = @)

Last modified: April 11, 2012

Research Interests

• Symbolic and Algebraic Computation
• Symbolic-Numeric Computation

Biography

1989.5 - 1994.6:
Research on computer-aided design for LSIs
1994.6 - 2000.3:
Research on symbolic and algebraic computation, symbolic-numeric computation

Society Membership

• Information Processing Society of Japan (IPSJ)
• Japan Society for Symbolic and Algebraic Computation (JSSAC)
  
• The Institute of Electronics, Information and Communication Engineers (IEICE)
• The Japan Society for Industrial and Applied Mathematics (JSIAM)
  
• The Association for Computing Machinery (ACM)

Selected Publications

• 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.

• 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.
• H. Nakayama and H. Sekigawa, Deciding divisibility between polynomials with inexact coefficients, ACM Communications in Computer Algebra, Vol. 43, No. 3, Issue 169, pp. 91-94, 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.
• 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.
• H. Sekigawa, Combining Symbolic and Numeric Computation, (in Japanese), IPSJ Magazine, 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, pp. 311-317, 2008.
• H. Sekigawa, The Nearest Polynomial with a Zero in a Given Domain, Theoretical Computer Science, Vol. 409, pp. 282-291, 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.
• 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.
• 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, D. Wang and L. Zhi (eds.), Birkhaeuser, pp. 167-184, 2007.

• H. Sekigawa and K. Shirayanagi, Locating Real Multiple Zeros of a Real Interval Polynomial (in Japanese), Journal of Japan Society for Symbolic and Algebraic Computation, Vol. 13, No. 1, pp. 68-71, 2006.
• Y. Nakajima, Y. Kawano, and H. Sekigawa, Quantum Circuit Design (in Japanese), IPSJ Magazine, Vol. 47, No. 12, pp. 1335-1340, 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.
• H. Sekigawa and K. Shirayanagi, On the Location of Zeros of an Interval Polynomial (in Japanese), IEICE Trans. A, Vol. J89-A, No. 3, pp. 199-216, 2006.
• N. Harada, T. Moriya, H. Sekigawa, K. Shiaryanagi, and Y. Kamamoto, Lossless Compression of IEEE754 Floating-Point Signal in ISO/IEC MPEG-4 Audio Lossless Coding (ALS) (in Japanese), IEICE Trans. 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 & Computation, Vol. 6, No. 1, pp. 67-80, 2006.

• H. Sekigawa and K. Shirayanagi, On the Location of Zeros of a Real Interval Polynomial (in Japanese), Journal of Japan Society for Symbolic and Algebraic Computation, 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 (ASCM2005), pp. 231-234, 2005.
• H. Nakajima, Y. Kawano, and 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.
• Y. Kawano, K. Kimura, H. Sekigawa, M. Noro, and K. Shirayanagi, Exact CNOT on an Exchange-Only Quantum Computer (in Japanese), Journal of Japan Society for Symbolic and Algebraic Computation, 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. Shiaryanagi, Lossless Compression of IEEE Floating-point Audio using Approximate Common Factor Coding and Masked-LZ Compression, Poster presentation at AES 118th Convention, 2005.

• H. Sekigawa, Zero Determination of Algebraic Numbers using Approximate Computation (in Japanese), Bulletin of the Japan Society for Industrial and Applied Mathematics, Vol. 14, No. 4, pp. 75-78, 2004.
• K. Miyamoto, K. Ohya, H. Sekigawa, and K. Shirayanagi, An Efficient Method of Finding Auxiliary Lines in Automated Geometry Theorem Proving (in Japanese), Proc. of the RIMS Workshop "Computer Algebra--Design of Algorithms, Implementations and Applications," Kokyuroku 1395, pp. 157-163, Research Institute for Mathematical Sciences, Kyoto Univ., 2004.
• Y. Kawano, K. Kimura, and H. Sekigawa, On Quantum Gates in Decoherence-Free Subspaces (in Japanese), Technical Report of IEICE, COMP2004-23, pp. 33-39, 2004.

• K. Miyamoto, H. Sekigawa, K. Shirayanagi, and F. Machida, On a Method for Automated Generation of Readable Proofs in Euclidean Geometry (in Japanese), Proc. of the RIMS Workshop "Computer Algebra--Algorithms, Implementations and Applications," Kokyuroku 1335, pp. 20-27, Research Institute for Mathematical Sciences, Kyoto Univ., 2003.

• K. Shirayanagi and H. Sekigawa, New Scientific Computing--Symbolic-Numeric Algebra (in Japanese), 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, Josai Information Sciences Researches, Vol. 9, No. 1, pp. 83-99, 1998.

• K. Shirayanagi and H. Sekigawa, An Interval Method Based on Zero Rewriting and its Application to Sturm's Algorithm (in Japanese), IEICE Trans. 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).