Symbolic-numeric Computation

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ISBN: 9783764379834 | 3764379839
Cover: Hardcover
Copyright: 3/6/2007

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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 27 research articles on the integration and interaction of symbolic and numeric computation.

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On a generalized companion matrix pencil for matrix polynomials expressed in the Lagrange basis	p. 1
Ill-conditioned properties and hybrid computations	p. 17
Rational interpolation and its Ill-conditioned property	p. 47
Computing approximate GCD of multivariate polynomials	p. 55
Structured low rank approximation of a Sylvester matrix	p. 69
Implementation of fast low rank approximation of a Sylvester matrix	p. 85
New algorithms for exact and approximate polynomial decomposition	p. 99
Amortized bound for root isolation via sturm sequences	p. 113
An algorithm of real root isolation for polynomial systems with applications to the construction of limit cycles	p. 131
An algebraic method for separating close-root clusters and the minimum root separation	p. 149
On the location of zeros of an interval polynomial	p. 167
Root-finding with Eigen-solving	p. 185
Galois theory via eigenvalue methods	p. 211
Pythagore's dilemma, symbolic-numeric computation, and the border basis method	p. 223
Proposal for the algorithmic use of the BKK-number in the algebraic reduction of a O-dimensional polynomial system	p. 245
Evaluation of Jacobian matrices for Newton's method with deflation to approximate isolated singular solutions of polynomial systems	p. 269
On approximate linearized triangular decompositions	p. 279
On the extended iterative proportional scaling algorithm	p. 299
Preprocessing for finite element discretizations of geometric problems	p. 315
Symbolic computation sequences and numerical analytic geometry applied to multibody dynamical systems	p. 335
A symbolic-numeric approach to an electric field problem	p. 349
Financial applications of symbolically generated compact finite difference formulae	p. 361
Symbolic analyzer for large lumped and distributed networks	p. 375
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Symbolic-numeric Computation

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