## 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

On a Generalized Companion Matrix Pencil for Matrix Polynomials | 1 |

Illconditioned Properties and Hybrid Computations | 17 |

Rational Interpolation and Its Illconditioned Property 47 | 46 |

Structured Low Rank Approximation of a Sylvester Matrix _ _ _ _ _ _ | 69 |

Implementation of Fast Low Rank Approximation of a Sylvester Matrix _ _ 85 | 84 |

New Algorithms for Exact and Approximate Polynomial Decomposition | 99 |

Amortized Bound for Root Isolation via Sturm Sequences | 113 |

An Algorithm of Real Root Isolation for Polynomial Systems with | 130 |

Galois Theory via Eigenvalue Methods | 211 |

Pythagores Dilemma SymbolicNumeric Computation and the Border | 223 |

Proposal for the Algorithmic Use of the BKKNumber in the Algebraic | 244 |

Evaluation of Jacobian Matrices for Newtons Method with Deﬂation | 269 |

On the Extended Iterative Proportional Scaling Algorithm | 299 |

Preprocessing for Finite Element Discretizations of Geometric Problems 315 | 314 |

Symbolic Computation Sequences and Numerical Analytic Geometry | 335 |

A SymbolicNumeric Approach to an Electric Field Problem 349 | 348 |

An Algebraic Method for Separating CloseRoot Clusters and | 149 |

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

RootFinding with EigenSolving | 185 |

Symbolic Analyzer for Large Lumped and Distributed Networks | 375 |

395 | |

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accuracy ACM Press Algebraic Geometry American option analysis AppGCD applied approximate GCD border basis border monomials close roots cluster coefﬁcients coeﬁicients compact ﬁnite difference companion matrix complex condition number convergence Corless decomposition deﬁation deﬁned deﬁnition degree denote discrete DPR1 edges eigen-solvers eigenvalues error evaluation example factor ﬁeld ﬁnd ﬁnite difference method ﬁnite element ﬁrst free boundary values Gaussian elimination GC matrices given HRFA hybrid ill-conditioned input integral irreducible iterative proportional scaling Kaltofen Lemma linear Math Mathematics monic polynomials multiple 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 satisﬁes Sect SIAM singular value Singular Value Decomposition solution solve step structure Sturm sequence support-leading Sylvester matrix symbolic computation Symbolic-Numeric Computation Theorem undesired zero variables vector zero and pole