Symbolic-Numeric Computation

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Dongming Wang, Li-Hong Zhi
Springer Science & Business Media, Jun 25, 2007 - Mathematics - 395 pages
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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. 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 Expressed in the Lagrange Basis
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
Author Index
395
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