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Symbolic-Numeric Computation

  • Conference proceedings
  • © 2007

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Overview

Editors:
  1. Dongming Wang

    1. School of Science, Beihang University, Beijing, China
      Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie - CNRS, Paris, France

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  2. Lihong Zhi

    1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Sciences, Beijing, China

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  • Inspired by the International Workshop on Symbolic-Numeric Computation 2005, Xi'an, China

Part of the book series: Trends in Mathematics (TM)

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About this book

The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations, two types of computation coexisting in mathematics yet separated in traditional research of mathematical computation. This book presents 23 research articles on the integration and interaction of symbolic and numeric computation.

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Table of contents (23 papers)

  1. Front Matter

    Pages i-viii
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  2. On a Generalized Companion Matrix Pencil for Matrix Polynomials Expressed in the Lagrange Basis

    • Robert M. Corless
    Pages 1-15
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  3. Ill-conditioned Properties and Hybrid Computations

    • Matu-Tarow Noda
    Pages 17-45
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  4. Rational Interpolation and Its Ill-conditioned Property

    • Hiroshi Kai
    Pages 47-53
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  5. Computing Approximate GCD of Multivariate Polynomials

    • Masaru Sanuki
    Pages 55-68
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  6. Structured Low Rank Approximation of a Sylvester Matrix

    • Erich Kaltofen, Zhengfeng Yang, Lihong Zhi
    Pages 69-83
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  7. Implementation of Fast Low Rank Approximation of a Sylvester Matrix

    • Bingyu Li, Zhuojun Liu, Lihong Zhi
    Pages 85-97
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  8. New Algorithms for Exact and Approximate Polynomial Decomposition

    • Mark Giesbrecht, John May
    Pages 99-112
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  9. Amortized Bound for Root Isolation via Sturm Sequences

    • Zilin Du, Vikram Sharma, Chee K. Yap
    Pages 113-129
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  10. An Algorithm of Real Root Isolation for Polynomial Systems with Applications to the Construction of Limit Cycles

    • Zhengyi Lu, Bi He, Yong Luo, Lu Pan
    Pages 131-147
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  11. An Algebraic Method for Separating Close-Root Clusters and the Minimum Root Separation

    • Tateaki Sasaki, Fujio Kako
    Pages 149-166
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  12. On the Location of Zeros of an Interval Polynomial

    • Hiroshi Sekigawa, Kiyoshi Shirayanagi
    Pages 167-184
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  13. Root-Finding with Eigen-Solving

    • Victor Y. Pan, Brian Murphy, Rhys Eric Rosholt, Dmitriy Ivolgin, Yuqing Tang, Xiaodong Yan et al.
    Pages 185-210
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  14. Galois Theory via Eigenvalue Methods

    • David A. Cox
    Pages 211-222
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  15. Pythagore’s Dilemma, Symbolic-Numeric Computation, and the Border Basis Method

    • Bernard Mourrain
    Pages 223-243
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  16. Proposal for the Algorithmic Use of the BKK-Number in the Algebraic Reduction of a O-dimensional Polynomial System

    • Hans J. Stetter
    Pages 245-267
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  17. Evaluation of Jacobian Matrices for Newton’s Method with Deflation to Approximate Isolated Singular Solutions of Polynomial Systems

    • Anton Leykin, Jan Verschelde, Ailing Zhao
    Pages 269-278
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  18. On Approximate Linearized Triangular Decompositions

    • Marc Moreno Maza, Greg J. Reid, Robin Scott, Wenyuan Wu
    Pages 279-298
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  19. On the Extended Iterative Proportional Scaling Algorithm

    • Ming-Deh Huang, Qing Luo
    Pages 299-313
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  20. Preprocessing for Finite Element Discretizations of Geometric Problems

    • Hong Gu, Martin Burger
    Pages 315-333
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Editors and Affiliations

  • School of Science, Beihang University, Beijing, China

    Dongming Wang

  • Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie - CNRS, Paris, France

    Dongming Wang

  • Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Sciences, Beijing, China

    Lihong Zhi

Bibliographic Information

  • Book Title: Symbolic-Numeric Computation

  • Editors: Dongming Wang, Lihong Zhi

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-7643-7984-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2007

  • Hardcover ISBN: 978-3-7643-7983-4Published: 22 January 2007

  • eBook ISBN: 978-3-7643-7984-1Published: 25 June 2007

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: VIII, 395

  • Topics: Numerical Analysis

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