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 booklet presents an intensive advent to numerical computing from the perspective of backward blunders research. The meant viewers comprises scholars and researchers in technology, engineering and arithmetic. The procedure taken is a bit casual because of the wide range of backgrounds of the readers, however the significant 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 machine evaluate of capabilities; half II covers numerical linear algebra; half III covers interpolation, the FFT and quadrature; and half IV covers numerical options of differential equations together with initial-value difficulties, boundary-value difficulties, hold up differential equations and a short bankruptcy on partial differential equations.

The publication comprises distinctive illustrations, bankruptcy summaries and various workouts to boot a few Matlab codes supplied on-line as supplementary material.

“I relatively just like the concentrate on backward errors research and . this can be novel in a textbook and a pragmatic technique that might carry welcome attention." Lawrence F. Shampine

A Graduate creation to Numerical equipment and Backward mistakes research” has been chosen by way of Computing experiences as a outstanding booklet in computing in 2013. Computing studies better of 2013 checklist involves ebook and article nominations from reviewers, CR classification editors, the editors-in-chief of journals, and others within the computing community.

Show description

Read or Download A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis PDF

Best introduction books

Download e-book for iPad: An Introduction to Multivariate Statistical Analysis (Wiley by T. W. Anderson

Perfected over 3 variations and greater than 40 years, this box- and classroom-tested reference:* makes use of the tactic of extreme chance to a wide volume to make sure moderate, and from time to time optimum tactics. * Treats the entire uncomplicated and significant subject matters in multivariate information. * provides new chapters, in addition to a couple of new sections.

Read e-book online Introduction to analytical gas chromatography PDF

Overlaying the foundations of chromatographic separation, the chromatographic technique from a actual chemical viewpoint, instrumentation for acting analyses, and operational tactics, this moment variation deals details wanted for the profitable perform of gasoline chromatography. It comprises examples of accessible gear, detectors, columns, desk bound stages and working stipulations.

Download e-book for iPad: Nanotechnology: An Introduction to Nanostructuring by Prof. Dr. Michael Kohler, Dr. Wolfgang Fritzsche(auth.)

Content material: bankruptcy 1 creation (pages 1–11): bankruptcy 2 Molecular fundamentals (pages 13–31): bankruptcy three Microtechnological Foundations (pages 33–85): bankruptcy four guidance of Nanostructures (pages 87–148): bankruptcy five Nanotechnical buildings (pages 149–209): bankruptcy 6 Characterization of Nanostructures (pages 211–224): bankruptcy 7 Nanotransducers (pages 225–269): bankruptcy eight Technical Nanosystems (pages 271–282):

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

Sample text

283 The implicit curves 25xy = 12 and x2 + y2 = 1 . . . . . . . . . . . 3 Scaled residuals for the Richardson iteration of a 5 × 5 matrix . . . . 314 Scaled residuals for the Richardson iteration of a 89 × 89 matrix . . . 315 Nine hundred ninety-nine eigenvalues of a random 1, 000 × 1, 000 real matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The problem of interpolation. (a) Data of the problem. In some cases, we also have some values of f (k) (τ ).

If we let x ∈ R and : R → F be an operator for the standard rounding procedure to the nearest floating-point number4 (see Appendix A), then the absolute representation error Δ x is Δx = x − x = xˆ − x . ) If x = 0, the relative representation error δ x is given by δx = Δ x xˆ − x = . 2) From those two definitions, we obtain the following useful equality if x = 0: xˆ = x + Δ x = x(1 + δ x) . 3) The IEEE standard described in Appendix A guarantees that |δ x| < μM , where μM is half the machine epsilon εM .

1) with ode45 . . . . 521 Scaled residual components of the Lorenz system . . . . . . . . . 5 . . . . . . . 525 Commutative diagram for the backward error analysis of initial-value problems . . . . . . . . . . . . . . . . . . . . 29) with ode45. (a) Absolute residual in x1 . (b) Absolute residual in x2 . (c) Relative residual in the six components of y. (d) Condition number of the problem . . . . . . . 537 An xkcd comic . . . . . . .

Download PDF sample

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


by Mark
4.2

Rated 4.20 of 5 – based on 36 votes