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Numerical and Symbolic Scientific Computing

Progress and Prospects

Ulrich Langer, Peter Paule (Herausgeber)

Buch | Softcover

VIII, 358 Seiten

2011 | 2012
Springer Wien (Verlag)
978-3-7091-0793-5 (ISBN)

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The book presents the state of the art, new results, and it also includes articles pointing to future developments. Most of the articles center around the theme of partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Fast solvers and a posteriori error estimates in elastoplasticity. - Symbolic analysis for boundary problems: from rewriting to parametrized Groebner Bases. - approximate implicitization of space curves. - A symbolic-numeric algorithm for genus computation. - Linear partial differential equations and linear partial differential operators in computer algebra. - Computer algebra meets finite elements: an efficient implementation for Maxwell's Equations. - Sound and compelte verificcation condition generator for functional recursive programs. - Analytical evaluations of double integral expressions related to total variation. - A symbolic approach to generation and analysis of finite difference schemes of partial differential equations. - The "Seven Dwarfs" of symbolic computation. - An introduction to automated discovery in geometry through symbolic computation. - White noise analysis for stochastic partial differential equations. - Computing smoothing rates of collective point smoothers for optimal control problems using symbolic computation. - Sparsity optimized high-order finite element functions on simplices.

Erscheint lt. Verlag	19.11.2011
Reihe/Serie	Texts & Monographs in Symbolic Computation
Zusatzinfo	VIII, 358 p. 50 illus., 13 illus. in color.
Verlagsort	Vienna
Sprache	englisch
Maße	155 x 235 mm
Gewicht	555 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Algebra • applied geometry • computational mathematics • Numerical analysis • Scientific Computing • Symbolic Computation
ISBN-10	3-7091-0793-8 / 3709107938
ISBN-13	978-3-7091-0793-5 / 9783709107935
Zustand	Neuware