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| 2009
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1
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An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination
Hidenao Iwane, Hitoshi Yanami, Hirokazu Anai, Kazuhiro Yokoyama
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August 2009
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SNC '09: Proceedings of the 2009 conference on Symbolic numeric computation
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Publisher: ACM
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Full text available: |
 Pdf
(608.86 KB)
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| Bibliometrics: Downloads (6 Weeks): 2, Downloads (12 Months): 4, Citation Count: 0 |
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Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are ...
Keywords: certified numerical computation, cylindrical algebraic decomposition, dynamic evaluation, quantifier elimination, symbolic-numeric computation
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2
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Solution of algebraic riccati equations using the sum of roots
Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara
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July 2009
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ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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Publisher: ACM
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Full text available: |
Pdf
(525.17 KB)
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| Bibliometrics: Downloads (6 Weeks): 6, Downloads (12 Months): 22, Citation Count: 0 |
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This paper constructs an algebraic solution approach to the algebraic Riccati equation, an important equation in signal processing and control system design. Key features of the proposed approach are the exploitation of useful structures inherent in ...
Keywords: algebraic riccati equation, control theory, gröbner basis, polynomial spectral factorization, sum of roots
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3
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Computation schemes for splitting fields of polynomials
Sébastien Orange, Guénaël Renault, Kazuhiro Yokoyama
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July 2009
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ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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Publisher: ACM
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Full text available: |
Pdf
(705.81 KB)
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| Bibliometrics: Downloads (6 Weeks): 4, Downloads (12 Months): 23, Citation Count: 0 |
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In this article, we present new results about the computation of a general shape of a triangular basis generating the splitting ideal of an irreducible polynomial given with the permutation representation of its Galois group G. We provide some ...
Keywords: galois theory, splitting field, triangular set
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4
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Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem
Hirokazu Anai, Shinji Hara, Masaaki Kanno, Kazuhiro Yokoyama
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July 2009
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Journal of Symbolic Computation
, Volume 44 Issue 7
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Publisher: Academic Press, Inc.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 1 |
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This paper presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Grobner bases and polynomial spectral ...
Keywords: Gröbner basis, H2 control, Parametric optimization, Parametric polynomial spectral factorization, Quantifier elimination, Sum of roots
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5
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| 2008
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6
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Multi-modular algorithm for computing the splitting field of a polynomial
Guénaël Renault, Kazuhiro Yokoyama
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July 2008
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ISSAC '08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
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Publisher: ACM
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Full text available: |
Pdf
(327.71 KB)
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| Bibliometrics: Downloads (6 Weeks): 5, Downloads (12 Months): 38, Citation Count: 1 |
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Let f be a univariate monic integral polynomial of degree n and let (α1, ..., αn) be an n-tuple of its roots in an algebraic closure Q of Q. Obtaining an algebraic representation of the splitting field Q(α1, ...
Keywords: galois theory, splitting field
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7
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Symbolic optimization of algebraic functions
Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara
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July 2008
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ISSAC '08: Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
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Publisher: ACM
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Full text available: |
Pdf
(370.80 KB)
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| Bibliometrics: Downloads (6 Weeks): 6, Downloads (12 Months): 63, Citation Count: 0 |
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This paper attempts to establish a new framework of symbolic optimization of algebraic functions that is relevant to possibly a wide variety of practical application areas. The crucial aspects of the framework are (i) the suitable use of algebraic methods ...
Keywords: groebner basis, parametric optimization, polynomial spectral factorization, quantifier elimination
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| 2007
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8
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On systems of algebraic equations with parametric exponents II
Kazuhiro Yokoyama
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November 2007
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Applicable Algebra in Engineering, Communication and Computing
, Volume 18 Issue 6
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Publisher: Springer-Verlag
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0 |
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We deal with ideals generated by polynomials with parametric exponents, and discuss certain stability of forms of Gröbner bases of those ideals. Based on the author’s previous work, we investigate techniques by “slack variables” ...
Keywords: Gröbner basis, Ideals with parametric exponents
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9
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Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization
Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara
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July 2007
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ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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Publisher: ACM
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Full text available: |
Pdf
(279.76 KB)
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| Bibliometrics: Downloads (6 Weeks): 5, Downloads (12 Months): 29, Citation Count: 2 |
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This paper proposes an algebraic approach for parametric optimization which can be utilized for various problems in signal processing and control.The approach exploits the relationship between the sum of roots and polynomial spectral factorization and ...
Keywords: Gröbner basis, parametric optimization, polynomial spectral factorization, quantifier elimination, H 2 control, sum of roots
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| 2005
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10
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Sum of roots with positive real parts
Hirokazu Anai, Shinji Hara, Kazuhiro Yokoyama
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July 2005
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ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation
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Publisher: ACM
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Full text available: |
Pdf
(376.65 KB)
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| Bibliometrics: Downloads (6 Weeks): 5, Downloads (12 Months): 19, Citation Count: 6 |
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In this paper we present a method to compute or estimate the sum of roots with positive real parts (SORPRP) of a polynomial, which is related to a certain index of "average" stability in optimal control, without computing explicit numerical values of ...
Keywords: Gröbner basis, optimal regulator control, quantifier elimination, resultant, sum of roots with positive real parts
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