Description
Birkhauser Symbolic-Numeric Computation 2007 Edition by Dongming Wang Li-Hong Zhi
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. Table of contents : On a Generalized Companion Matrix Pencil for Matrix Polynomials Expressed in the Lagrange Basis.- Ill-conditioned Properties and Hybrid Computations.- Rational Interpolation and Its Ill-conditioned Property.- Computing Approximate GCD of Multivariate Polynomials.- Structured Low Rank Approximation of a Sylvester Matrix.- Implementation of Fast Low Rank Approximation of a Sylvester Matrix.- New Algorithms for Exact and Approximate Polynomial Decomposition.- Amortized Bound for Root Isolation via Sturm Sequences.- An Algorithm of Real Root Isolation for Polynomial Systems with Applications to the Construction of Limit Cycles.- An Algebraic Method for Separating Close-Root Clusters and the Minimum Root Separation.- On the Location of Zeros of an Interval Polynomial.- Root-Finding with Eigen-Solving.- Galois Theory via Eigenvalue Methods.- Pythagore's Dilemma Symbolic-Numeric Computation and the Border Basis Method.- Proposal for the Algorithmic Use of the BKK-Number in the Algebraic Reduction of a O-dimensional Polynomial System.- Evaluation of Jacobian Matrices for Newton's Method with Deflation to Approximate Isolated Singular Solutions of Polynomial Systems.- On Approximate Linearized Triangular Decompositions.- On the Extended Iterative Proportional Scaling Algorithm.- Preprocessing for Finite Element Discretizations of Geometric Problems.- Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical Systems.- A Symbolic-Numeric Approach to an Electric Field Problem.- Financial Applications of Symbolically Generated Compact Finite Difference Formulae.- Symbolic Analyzer for Large Lumped and Distributed Networks.