Symbolic-Numeric Computation

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Dongming Wang, Li-Hong Zhi
Springer Science & Business Media, Jan 22, 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
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
Author Index
395
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