Synopses & Reviews
Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming ("the Hamming code," "the Hamming distance," and "Hamming window," etc.), suggests that the purpose of computing is insight, not merely numbers. In that connection he outlines five main ideas that aim at producing meaningful numbers that will be read and used, but will also lead to greater understanding of how the choice of a particular formula or algorithm influences not only the computing but our understanding of the results obtained.
The five main ideas involve (1) insuring that in computing there is an intimate connection between the source of the problem and the usability of the answers (2) avoiding isolated formulas and algorithms in favor of a systematic study of alternate ways of doing the problem (3) avoidance of roundoff (4) overcoming the problem of truncation error (5) insuring the stability of a feedback system.
In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include:
I. Fundamentals and Algorithms
II. Polynomial Approximation- Classical Theory
Ill. Fourier Approximation- Modern Theory
IV. Exponential Approximation ... and more
Highly regarded by experts in the field, this is a book with unlimited applications for undergraduate and graduate students of mathematics, science and engineering. Professionals and researchers will find it a valuable reference they will turn to again and again.
Synopsis
For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten, and enlarged the material. Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.
Synopsis
This inexpensive paperback edition of a groundbreaking text stresses frequency approach in coverage of algorithms, polynomial approximation, Fourier approximation, exponential approximation, and other topics. Revised and enlarged 2nd edition.
Synopsis
This inexpensive paperback edition of a groundbreaking text stresses frequency approach in coverage of algorithms, polynomial approximation, Fourier approximation, exponential approximation, other topics. Revised and enlarged 2nd edition.
About the Author
Richard W. Hamming: The Computer Icon
Richard W. Hamming (1915-1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004.
In the Author's Own Words:
"The purpose of computing is insight, not numbers."
"There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think."
"Whereas Newton could say, 'If I have seen a little farther than others, it is because I have stood on the shoulders of giants, I am forced to say, 'Today we stand on each other's feet.' Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way."
"If you don't work on important problems, it's not likely that you'll do important work." — Richard W. Hamming
Table of Contents
Preface
I Fundamentals and Algorithms
1 An Essay on Numerical Methods
2 Numbers
3 Function Evaluation
4 Real Zeros
5 Complex Zeros
*6 Zeros of Polynomials
7 Linear Equations and Matrix Inversion
*8 Random Numbers
9 The Difference Calculus
10 Roundoff
*11 The Summation Calculus
*12 Infinite Series
13 Difference Equations
II Polynomial Approximation-Classical Theory
14 Polynomial Interpolation
15 Formulas Using Function Values
16 Error Terms
17 Formulas Using Derivatives
18 Formulas Using Differences
*19 Formulas Using the Sample Points as Parameters
20 Composite Formulas
21 Indefinite Integrals-Feedback
22 Introduction to Differential Equations
23 A General Theory of Predictor-Corrector Methods
24 Special Methods of Integrating Ordinary Differential Equations
25 Least Squares: Practice Theory
26 Orthogonal Functions
27 Least Squares: Practice
28 Chebyshev Approximation: Theory
29 Chebyshev Approximation: Practice
*30 Rational Function Approximation
III Fournier Approximation-Modern Theory
31 Fourier Series: Periodic Functions
32 Convergence of Fourier Series
33 The Fast Fourier Transform
34 The Fourier Integral: Nonperiodic Functions
35 A Second Look at Polynomial Approximation-Filters
*36 Integrals and Differential Equations
*37 Design of Digital Filters
*38 Quantization of Signals
IV Exponential Approximation
39 Sums of Exponentials
*40 The Laplace Transform
*41 Simulation and the Method of Zeros and Poles
V Miscellaneous
42 Approximations to Singularities
43 Optimization
44 Linear Independence
45 Eigenvalues and Eigenvectors of Hermitian Matrices
N + 1 The Art of Computing for Scientists and Engineers
Index
* Starred sections may be omitted.