Computer Algebra in Scientific Computing: Casc 2000

ISBN-13: 9783642624902 / Angielski / Miękka / 2014 / 439 str.

Viktor G. Ganzha; Ernst Mayr; Evgenii Vorozhtsov

Opis

The book covers various topics of computer algebra methods, algorithms and software applied to scientific computing. One of the important topics of the book is the application of computer algebra methods for the development of new efficient analytic and numerical solvers, both for ordinary and partial differential equations. A specific feature of the book is a detailed analysis of the advanced software systems like Mathematica, Maple etc. from the viewpoint of their applicability for the solution of scientific computing problems. The book will be useful for researchers and engineers who apply the advanced computer algebra methods for the solution of their tasks.

Spis treści

Fast Matrix Computation of Subresultant Polynomial Remainder Sequences.- About Simultaneous Representation of Two Natural Numbers by a Sum of Three Primes.- On a Description of Irreducible Component in the Set of Nilpotent Leibniz Algebras Containing the Algebra of Maximal Nilindex, and Classification of Graded Filiform Leibniz Algebras.- Application of Computer Algebra in Problems on Stabilization of Gyroscopic Systems.- Implementing Computational Services Based on OpenMath.- Group Classification of the Navier-Stokes Equations for Compressible Viscous Heat-Conducting Gas.- Plotting Functions and Singularities with Maple and Java on a Component-based Web Architecture.- Stable Self-Oscillatory Regimes in Volterra Models of Three Populations.- Computing “Small” 1-Homological Models for Commutative Differential Graded Algebras.- Effective computation of algebra of derivations of Lie algebras.- An Integration and Reduction for Ordinary Non Linear Differential Equations Library.- Complexity of Derivatives Generated by Symbolic Differentiation.- An Assessment of the Efficiency of Computer Algebra Systems in the Solution of Scientific Computing Problems.- On the Relation Between Pommaret and Janet Bases.- An (Asymptotic) Error Bound for the Evaluation of Polynomials at Roots.- Three Remarks on Comprehensive Gröbner and SAGBI Bases.- Computing the Cylindrical Algebraic Decomposition Adapted to a Set of Equalities.- Symbolic Algorithms of Algebraic Perturbation Theory for a Hydrogen Atom: the Stark Effect.- CADECOM: Computer Algebra software for functional DECOMposition.- Computeralgebra and the Systematic Construction of Finite Unlabeled Structures.- Heat Invariant E2 for Nonminimal Operator on Manifolds with Torsion.- Computer Algebra for Automated Performance Modeling of Fortran Programs.- A Parallel Symbolic-Numerical Approach to Algebraic Curve Plotting.- Parametric Analysis for a Nonlinear System.- Extended Splicing System and Semigroup of Dominoes.- Newton Polyhedra and the Reversible System of Ordinary Differential Equations.- Condition Analysis of Overdetermined Algebraic Problems.- An Algebraic Approach to Offsetting and Blending of Solids.- Application of Computer Algebra Methods to Some Problems of Theoretical and Applied Celestial Mechanics.- Computing the Frobenius Normal Form of a Sparse Matrix.- Lessons Learned from Using CORBA for Components in Scientific Computing.- Deciding Linear-Transcendental Problems.- Author Index.

O autorze

Prof. Dr. Victor Ganzha lehrt am Fachbereich Mathematik/Informatik der Universität-GH Kassel. Er beschäftigt sich mit symbolisch-numerischen Methoden.