## Symbolic-Numeric ComputationThe growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation. |

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### Contents

1 | |

Illconditioned Properties and Hybrid Computations | 17 |

Rational Interpolation and Its Illconditioned Property | 46 |

Computing Approximate GCD of Multivariate Polynomials | 55 |

Structured Low Rank Approximation of a Sylvester Matrix | 69 |

Implementation of Fast Low Rank Approximation of a Sylvester Matrix | 84 |

New Algorithms for Exact and Approximate Polynomial Decomposition | 99 |

Amortized Bound for Root Isolation via Sturm Sequences | 113 |

Pythagores Dilemma SymbolicNumeric Computation and the Border Basis Method | 223 |

Proposal for the Algorithmic Use of the BKKNumber in the Algebraic Reduction of a 0dimensional Polynomial System | 244 |

Evaluation of Jacobian Matrices for Newtons Method with Deflation to Approximate Isolated Singular Solutions of Polynomial Systems | 269 |

On Approximate Linearized Triangular Decompositions | 279 |

On the Extended Iterative Proportional Scaling Algorithm | 299 |

Preprocessing for Finite Element Discretizations of Geometric Problems | 314 |

Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical Systems | 335 |

A SymbolicNumeric Approach to an Electric Field Problem | 348 |

for Polynomial Systems with Applications to the Construction of Limit Cycles | 130 |

An Algebraic Method for Separating CloseRoot Clusters and the Minimum Root Separation | 149 |

On the Location of Zeros of an Interval Polynomial | 167 |

RootFinding with EigenSolving | 185 |

Galois Theory via Eigenvalue Methods | 211 |

Financial Applications of Symbolically Generated Compact Finite Difference Formulae | 361 |

Symbolic Analyzer for Large Lumped and Distributed Networks | 375 |

395 | |

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### Common terms and phrases

accuracy ACM Press analysis AppGCD applied approximate GCD border basis border monomials close roots cluster coefficients compact finite difference companion matrix complex condition number consider convergence Corless decomposition deflation degree denote discrete DPR1 edges eigen-solvers eigenvalues error evaluation example factor finite difference method finite element formula free boundary values Galois Galois group Gaussian elimination GC matrices given Gröbner Gröbner basis HRFA hybrid ill-conditioned input integral irreducible iterative proportional scaling Kaltofen Lemma Maple Math monic polynomials multiple multivariate polynomial nodes normal set numerical numerical stability obtain parameters PC-PRS algorithm perturbation polynomial equations polynomial f polynomial system problem Proc Proof pseudozeros quotient ring rational function rational interpolant real root isolation root-finders Sect SIAM singular value Singular Value Decomposition solution solve splitting field step structure Sturm sequence Sylvester matrix symbolic computation symbolic-numeric Symbolic—Numeric Computation Theorem undesired zero variables vector zero and pole