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By Robert M. Corless
This booklet offers an intensive advent to numerical computing from the perspective of backward errors research. The meant viewers comprises scholars and researchers in technological know-how, engineering and arithmetic. The method taken is just a little casual because of the big variety of backgrounds of the readers, however the crucial principles of backward blunders and sensitivity (conditioning) are systematically emphasised. The ebook is split into 4 components: half I offers the historical past preliminaries together with floating-point mathematics, polynomials and computing device evaluate of features; half II covers numerical linear algebra; half III covers interpolation, the FFT and quadrature; and half IV covers numerical recommendations of differential equations together with initial-value difficulties, boundary-value difficulties, hold up differential equations and a quick bankruptcy on partial differential equations.
The ebook includes specified illustrations, bankruptcy summaries and various workouts besides a few Matlab codes supplied on-line as supplementary material.
“I particularly just like the concentrate on backward mistakes research and situation. this can be novel in a textbook and a realistic process that may deliver welcome attention." Lawrence F. Shampine
A Graduate creation to Numerical tools and Backward mistakes research” has been chosen through Computing experiences as a amazing ebook in computing in 2013. Computing reports better of 2013 checklist contains e-book and article nominations from reviewers, CR type editors, the editors-in-chief of journals, and others within the computing community.
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Additional info for A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis
Example text
10 Notes and References . . . . . . . . . . . . . . . . . . . 676 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 14 Numerical Solutions of Boundary Value Problems . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 2 Conditioning . . . . . . . . . . . . . . . . . . . . . . . 3 A Method to Solve BVPODE . . . . . . . .
4 Trigonometric interpolation . . . . . . . . . . . . . . . . . . . 409 A solution of the van der Pol equation . . . . . . . . . . . . . . 410 Periodogram for the van der Pol equation . . . . . . . . . . . . . 410 Periodogram for a forced van der Pol equation . . . . . . . . . . . 4 An approximation to a definite integral by a finite Riemann sum . . . 420 The graph of an integrand for W on 0 ≤ v ≤ π . . . . . . . . . . . 433 The graph of 1/(1 + u64 ) on 0 ≤ u ≤ 1 .
7 The Method of Modified Equations . . . . . . . . . . . . . . 1 Correlations and Structure in the Residual . . . . . . . 2 Finding a Modified Equation . . . . . . . . . . . . . 8 Geometric Integration . . . . . . . . . . . . . . . . . . . 9 Other Methods . . . . . . . . . . . . . . . . . . . . . . 10 Notes and References . . . . . . . . . . . . . . . . . . . 676 Problems .