A Graduate Introduction to Numerical Methods (PDF)
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This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations.
The book contains detailed illustrations, chapter summaries and a variety of exercises aswell as some Matlab codes provided online as supplementary material.
"I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine
- Autoren: Robert M. Corless , Nicolas Fillion
- 2013, 2014, 869 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 1461484537
- ISBN-13: 9781461484530
- Erscheinungsdatum: 12.12.2013
Abhängig von Bildschirmgrösse und eingestellter Schriftgrösse kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Grösse: 13 MB
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- Vorlesefunktion
“This book is intended to be a graduate introduction to numerical methods from the perspective of backward error analysis. … it is the variety of topics and case studies, both theoretical and numerical, presented in the book that is its strongest point, making it a valuable reference work for students and professionals … .” (Justin Steven C. Prentice, Mathematical Reviews, January, 2015)“This textbook provides a very readable and comprehensive graduate-level introduction to numerical methods and their analysis. … The textbook contains many references, exercises, MATLAB codes, and numerical illustrations. It is written in a style that is both informal and informative which makes this book unique in fact.” (Robert Plato, zbMATH, Vol. 1295, 2014)
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