A Graduate Introduction to Numerical Methods: From the by Robert M. Corless

By Robert M. Corless

This e-book offers an in depth creation to numerical computing from the point of view of backward blunders research. The meant viewers comprises scholars and researchers in technological know-how, engineering and arithmetic. The technique taken is slightly casual as a result of the big variety of backgrounds of the readers, however the primary principles of backward errors and sensitivity (conditioning) are systematically emphasised. The publication is split into 4 elements: half I offers the historical past preliminaries together with floating-point mathematics, polynomials and laptop evaluate of features; half II covers numerical linear algebra; half III covers interpolation, the FFT and quadrature; and half IV covers numerical suggestions of differential equations together with initial-value difficulties, boundary-value difficulties, hold up differential equations and a quick bankruptcy on partial differential equations.

The publication comprises distinct illustrations, bankruptcy summaries and quite a few workouts in addition a few Matlab codes supplied on-line as supplementary material.

“I quite just like the specialize in backward blunders research and . this is often novel in a textbook and a pragmatic technique that would deliver welcome attention." Lawrence F. Shampine

A Graduate creation to Numerical equipment and Backward mistakes research” has been chosen by means of Computing stories as a striking publication in computing in 2013. Computing reports better of 2013 checklist comprises publication and article nominations from reviewers, CR classification editors, the editors-in-chief of journals, and others within the computing community.

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Additional resources for A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis

Sample text

676 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 14 Numerical Solutions of Boundary Value Problems . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 2 Conditioning . . . . . . . . . . . . . . . . . . . . . . . 3 A Method to Solve BVPODE . . . . . . . . . . . . . . . . 1 Solution on a Uniform Mesh . . . . . . . . . .

745 The computed eigenvalues of A (when n = 10) . . . . . . . . . . 17) . . . . . . . 748 Solution to yt (t) = −y(t − 1)/5, with jump discontinuities in histories . . 12) with Chebfun . . . . . . . . . 7 An approximate solution to Eq. 1) . . . . . . . . . . . . . . 1) . . . . . . 1) . . . 4) . . . . . . . . . . . . . 4) . . . . . . . . . . . 1) . . . . . 765 The solution to the one-way wave Eq. 8) . . . . . . .

72 The relative error S · exp(−x) − 1 in the truncated Chebyshev series . . 92 The relative error y · exp(−x) − 1 in the chebfun for y = exp(x) . . . 29 . . . . . . . . . . . . 2 Contours of the condition number of the Mandelbrot polynomial . . . 109 Fractal boundary for Newton’s map . . . . . . . . . . . . . . . 16 Condition of Wilkinson polynomial . . . . . . . . . . . . . . . 21) . . . . . 124 Error in a Chebyshev series approximation .

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