Symbolic-Numeric Computation

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

3. Ill-conditioned Properties and Hybrid Computations

   • Matu-Tarow Noda

   Pages 17-45

4. Rational Interpolation and Its Ill-conditioned Property

   • Hiroshi Kai

   Pages 47-53

5. Computing Approximate GCD of Multivariate Polynomials

   • Masaru Sanuki

   Pages 55-68

6. Structured Low Rank Approximation of a Sylvester Matrix

   • Erich Kaltofen, Zhengfeng Yang, Lihong Zhi

   Pages 69-83

7. Implementation of Fast Low Rank Approximation of a Sylvester Matrix

   • Bingyu Li, Zhuojun Liu, Lihong Zhi

   Pages 85-97

8. New Algorithms for Exact and Approximate Polynomial Decomposition

   • Mark Giesbrecht, John May

   Pages 99-112

9. Amortized Bound for Root Isolation via Sturm Sequences

   • Zilin Du, Vikram Sharma, Chee K. Yap

   Pages 113-129

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

11. An Algebraic Method for Separating Close-Root Clusters and the Minimum Root Separation

    • Tateaki Sasaki, Fujio Kako

    Pages 149-166

12. On the Location of Zeros of an Interval Polynomial

    • Hiroshi Sekigawa, Kiyoshi Shirayanagi

    Pages 167-184

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

14. Galois Theory via Eigenvalue Methods

    • David A. Cox

    Pages 211-222

15. Pythagore’s Dilemma, Symbolic-Numeric Computation, and the Border Basis Method

    • Bernard Mourrain

    Pages 223-243

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

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

18. On Approximate Linearized Triangular Decompositions

    • Marc Moreno Maza, Greg J. Reid, Robin Scott, Wenyuan Wu

    Pages 279-298

19. On the Extended Iterative Proportional Scaling Algorithm

    • Ming-Deh Huang, Qing Luo

    Pages 299-313

20. Preprocessing for Finite Element Discretizations of Geometric Problems

    • Hong Gu, Martin Burger

    Pages 315-333

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.

• Differential equations
• GCD computation
• Gröbner bases
• Numeric Computation
• Numeric polynomial algebra
• Symbolic Computation
• geometric computation
• geometry

• 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

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