Numerical Toolbox for Verified Computing I by Rolf Hammer
As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. This book is the first to offer a general discussion on • arithmetic and computational reliability, • analytical mathematics and verification techniques, • algorithms, and • (most importantly) actual implementations in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathematical prerequisites are universally held, we have tended towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. For all topics, we present exam ples, exercises, and numerical results demonstrating the application of the routines presented.-
Numerical Analysis for Elliptic Optimal Control Problems
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Introduction to Shape Optimization
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Numerical Methods for Two-phase Incompressible Flows
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Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
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Spectral Methods
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The Graduate Student's Guide to Numerical Analysis '98
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The Linearization Method for Constrained Optimization
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Hilbert Space Splittings and Iterative Methods
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The Concept of Stability in Numerical Mathematics
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Monotone Discretizations for Elliptic Second Order Partial Differential Equations
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Boundary Element Methods
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History of Continued Fractions and Padé Approximants
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Method of Difference Potentials and Its Applications
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Newton Methods for Nonlinear Problems
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High Order Difference Methods for Time Dependent PDE
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Logarithmic Norms
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Minimization Methods for Non-Differentiable Functions
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Hierarchical Matrices: Algorithms and Analysis
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Mixed and Hybrid Finite Element Methods
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Solving Elliptic Problems Using ELLPACK
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Discrete Iterations
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Numerical Techniques for Stochastic Optimization
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Numerical Continuation Methods
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Krylov Methods for Nonsymmetric Linear Systems
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Progress in Approximation Theory
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Sequence Transformations
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Nonlinear Approximation Theory
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Moduli of Smoothness
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Numerical Methods Based on Sinc and Analytic Functions
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Krylov Subspace Methods for Linear Systems
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Advanced Boundary Element Methods
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Retarded Potentials and Time Domain Boundary Integral Equations
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Numerical Modeling in Materials Science and Engineering
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Robust Numerical Methods for Singularly Perturbed Differential Equations
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Finite Element Methods for Incompressible Flow Problems
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Solving Ordinary Differential Equations I
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Solving Ordinary Differential Equations II
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Tensor Spaces and Numerical Tensor Calculus
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Matrix Iterative Analysis
| SKU | Unavailable |
| ISBN 13 | 9783642784255 |
| ISBN 10 | 3642784259 |
| Title | Numerical Toolbox for Verified Computing I |
| Author | Rolf Hammer |
| Series | Springer Series In Computational Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2011-12-08 |
| Number of pages | 339 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |