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Symbolic-Numeric Computation: Trends in Mathematics

Editat de Dongming Wang, Li-Hong Zhi
en Limba Engleză Hardback – 22 ian 2007
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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Specificații

ISBN-13: 9783764379834
ISBN-10: 3764379839
Pagini: 404
Ilustrații: VIII, 395 p.
Dimensiuni: 170 x 244 x 27 mm
Greutate: 0.88 kg
Ediția:2007
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Trends in Mathematics

Locul publicării:Basel, Switzerland

Public țintă

Research

Cuprins

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.

Textul de pe ultima copertă

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 with 23 chapters presents original research and tutorial survey on the integration and interaction of symbolic and numeric computations. It represents the current state of the art and will serve as a valuable reference on the development of algorithms and software packages for hybrid symbolic-numeric computation.
The book highlights the interaction between symbolic and numeric computations. It contains tutorial surveys by distinguished experts, covers recent advances on key topics, and provides effective methods illustrated with applications.

Caracteristici

Inspired by the International Workshop on Symbolic-Numeric Computation 2005, Xi'an, China