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Numerical and Symbolic Scientific Computing

Progress and Prospects

  • Book
  • © 2012

Overview

Editors:
  1. Ulrich Langer

    1. Inst. Numerische Mathematik, Universität Linz, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

  2. Peter Paule

    1. , Research Institute for Symbolic Computat, Johannes Kepler University, Linz, Austria

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Survey articles introduce to new methods connecting numerics and symbolic computation
  • New results in computational mathematics points out challenging future developments in scientific computing
  • Present state-of-the-art in this topic

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-viii
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  2. Approximate Implicitization of Space Curves

    • Martin Aigner, Bert Jüttler, Adrien Poteaux
    Pages 1-19

  3. Sparsity Optimized High Order Finite Element Functions on Simplices

    • Sven Beuchler, Veronika Pillwein, Joachim Schöberl, Sabine Zaglmayr
    Pages 21-44

  4. Fast Solvers and A Posteriori Error Estimates in Elastoplasticity

    • Peter G. Gruber, Johanna Kienesberger, Ulrich Langer, Joachim Schöberl, Jan Valdman
    Pages 45-63

  5. A Symbolic-Numeric Algorithm for Genus Computation

    • Mădălina Hodorog, Josef Schicho
    Pages 65-94

  6. The “Seven Dwarfs” of Symbolic Computation

    • Erich L. Kaltofen
    Pages 95-104

  7. Computer Algebra Meets Finite Elements: An Efficient Implementation for Maxwell’s Equations

    • Christoph Koutschan, Christoph Lehrenfeld, Joachim Schöberl
    Pages 105-121

  8. A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations

    • Viktor Levandovskyy, Bernd Martin
    Pages 123-156

  9. White Noise Analysis for Stochastic Partial Differential Equations

    • Hermann G. Matthies
    Pages 157-174

  10. Smoothing Analysis of an All-at-Once Multigrid Approach for Optimal Control Problems Using Symbolic Computation

    • Stefan Takacs, Veronika Pillwein
    Pages 175-191

  11. Analytical Evaluations of Double Integral Expressions Related to Total Variation

    • Carsten Pontow, Otmar Scherzer
    Pages 193-218

  12. Sound and Complete Verification Condition Generator for Functional Recursive Programs

    • Nikolaj Popov, Tudor Jebelean
    Pages 219-256

  13. An Introduction to Automated Discovery in Geometry through Symbolic Computation

    • Tomas Recio, María P. Vélez
    Pages 257-271

  14. Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases

    • Markus Rosenkranz, Georg Regensburger, Loredana Tec, Bruno Buchberger
    Pages 273-331

  15. Linear Partial Differential Equations and Linear Partial Differential Operators in Computer Algebra

    • Ekaterina Shemyakova, Franz Winkler
    Pages 333-358
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Keywords

About this book

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear 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.

Editors and Affiliations

  • Inst. Numerische Mathematik, Universität Linz, Linz, Austria

    Ulrich Langer

  • , Research Institute for Symbolic Computat, Johannes Kepler University, Linz, Austria

    Peter Paule

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