Computer Algebra in Scientific Computing

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

Klappentext
This book constitutes the refereed proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, held in Bonn, Germany, in September 2007. The volume is dedicated to Professor Vladimir P. Gerdt on the occasion of his 60th birthday. The 35 revised full papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in polynomial and matrix algebra, quantifier elimination, and Gröbner bases, as well as stability investigation of both differential equations and difference methods for them. Several papers are devoted to the application of computer algebra methods and algorithms to the derivation of new mathematical models in biology and in mathematical physics.

Inhalt
Analytic Solutions of Linear Difference Equations, Formal Series, and Bottom Summation.- Computations in Modules over Commutative Domains.- Advances on the Continued Fractions Method Using Better Estimations of Positive Root Bounds.- An Efficient LLL Gram Using Buffered Transformations.- On the Computation of A ???-Maps.- Algebraic Visualization of Relations Using RelView.- Comprehensive Triangular Decomposition.- Stability Investigation of a Difference Scheme for Incompressible Navier-Stokes Equations.- A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in the Magnetic Field: Cylindrical Coordinates.- An Algorithm for Construction of Normal Forms.- Computer Algebra: A 'Classical' Path to Explore Decoherence and Entanglement Phenomena in Quantum Information Theory.- Deducing the Constraints in the Light-Cone SU(3) Yang-Mills Mechanics Via Gröbner Bases.- On the Weight Spectra of Conway Matrices Related to the Non-transitive Head-or-Tail Game.- Properties of the Liapunov Stability Zones of the Lagrange Triangle.- Studying the Stability of the Second Order Non-autonomous Hamiltonian System.- On the Peculiar Properties of Families of Invariant Manifolds of Conservative Systems.- A Unified Algorithm for Multivariate Analytic Factorization.- On the Computation of the Defining Polynomial of the Algebraic Riccati Equation.- Symmetries and Dynamics of Discrete Systems.- Exact Solutions of Completely Integrable Systems and Linear ODE's Having Elliptic Function Coefficients.- Dynamics of Nonlinear Parabolic Equations with Cosymmetry.- Weak Integer Quantifier Elimination Beyond the Linear Case.- Polynomial Division Using Dynamic Arrays, Heaps, and Packed Exponent Vectors.- Ruppert Matrix as Subresultant Mapping.- Construction ofComputer System for Microobjects Recognition Based on Neural Networks.- Analytical Solution for Transient Flow of a Generalized Bingham Fluid with Memory in a Movable Tube Using Computer Algebra.- Some Elimination Problems for Matrices.- A Full System of Invariants for Third-Order Linear Partial Differential Operators in General Form.- Automatic Stability Analysis for a Diffusion Equation with Memories Using Maple.- Bounds for Real Roots and Applications to Orthogonal Polynomials.- Distance Computation from an Ellipsoid to a Linear or a Quadric Surface in IR n .- Robust Stability for Parametric Linear ODEs.- Symbolic and Algebraic Methods for Linear Partial Differential Operators.- A New Scheme for Deniable/Repudiable Authentication.- An Algebraic-Numeric Algorithm for the Model Selection in Kinetic Networks.- On the Representation of the Differential Operator in Bases of Periodic Coiflets and It's Application.