Download e-book for iPad: A Graduate Introduction to Numerical Methods: From the by Robert M. Corless

By Robert M. Corless

ISBN-10: 1461484529

ISBN-13: 9781461484523

ISBN-10: 1461484537

ISBN-13: 9781461484530

This ebook presents an in depth creation to numerical computing from the perspective of backward mistakes research. The meant viewers contains scholars and researchers in technology, engineering and arithmetic. The method taken is a bit casual due to the big variety of backgrounds of the readers, however the crucial rules of backward errors and sensitivity (conditioning) are systematically emphasised. The publication is split into 4 elements: half I offers the history preliminaries together with floating-point mathematics, polynomials and laptop evaluate of services; half II covers numerical linear algebra; half III covers interpolation, the FFT and quadrature; and half IV covers numerical ideas of differential equations together with initial-value difficulties, boundary-value difficulties, hold up differential equations and a quick bankruptcy on partial differential equations.

The e-book comprises specified illustrations, bankruptcy summaries and numerous workouts to boot a few Matlab codes supplied on-line as supplementary material.

“I particularly just like the concentrate on backward mistakes research and . this is often novel in a textbook and a realistic procedure that may carry welcome attention." Lawrence F. Shampine

A Graduate creation to Numerical equipment and Backward mistakes research” has been chosen through Computing reports as a awesome e-book in computing in 2013. Computing studies better of 2013 record comprises booklet and article nominations from reviewers, CR classification editors, the editors-in-chief of journals, and others within the computing community.

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

Example text

If the loop exits, Ai = AiTaylor(z). 3 Error Accumulation and Catastrophic Cancellation 17 10−6 Forward Error 10−8 10−10 10−12 10−14 10−16 10−18 −10 −8 −6 −4 t −2 0 2 Fig. 2 Error in a naive MATLAB implementation of the Taylor series computation of Ai 36 end Using this algorithm, can one expect to have a high accuracy, with error close to εM ? 2 displays the difference between the correct result (as computed with MATLAB’s function airy) and the naive Taylor series approach. 277. The solution is only accurate to two digits!

131 Forward error of a best approximant . . . . . . . . . . . . . . . 135 The contour L17 (z) − 1/Γ (z) = 10−8 exp(iθ ) . . . . . . . . . . . . 137 Conditioning of ln Γ on an interval . . . . . . . . . . . . . . . . 138 φ of the residuals for the secant method . . . . 143 Convergence ratios rn/rn−1 Inverse quadratic interpolation . . . . . . . . . . . . . . . . . 144 The error in the chebfun representation of ln(Γ (x)) on 3 ≤ x ≤ 4 .

789 Part V Afterword Part VI Appendices A Floating-Point Arithmetic . . . . . . . . . . . . . . . . . . . . 1 Number Representation . . . . . . . . . . . . . . . . . . 2 Operations and Roundoff . . . . . . . . . . . . . . . . . . 809 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 811 B Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . 1 Elementary Complex Arithmetic .

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A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis by Robert M. Corless


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