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am 24. März 1999
Throughout the book, that motto is repeated.
By reading and absorbing the material in this book, the reader is left with the tools and the insights necessary to derive their own numerical methods.
No longer will numerical methods be memorized as textbook formulas -- now the reader can adapt and derive a formula to solve a specific problem, instead of trying to fit one of a small number of textbook formulas to a problem.
The distinction is made between numerical analysis and numerical methods, with emphasis on the latter.
The book is roughly divided into two parts. The first part covers classical numerical methods, using classical error analysis (truncation error, roundoff error). The second part reexamines these methods under the frequency domain, analyzing how numerical methods affect various frequencies (the "transfer function" approach).
Numerical methods are derived under an information theory model, such as by finding a quadrature formula of the highest polynomial degree of accuracy, given limited information about the function and its derivatives.
Matrices and linear systems are not discussed as much as one might expect, although one chapter convincingly leads the reader to question some classical methods.
The content is well-rounded, introducing many readers to topics such as random number generators, difference equations and summation formulas, digital filters and quantization, discrete fourier transforms and the FFT, and orthogonal polynomials. A background in calculus is all that is needed.
Many real-world examples and anecdotes are cited, but without too much detail or too many illustrations given.
This book encourages the reader to ask: "What information is available about the problem? How can it be used to solve the problem? What are the limits of this information?" The approach is practical, not merely analytical.
This book teaches what most other numerical books fail to teach: How to derive your own formulas, and thus your own solutions to problems. And that is perhaps the most important lesson of all.
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am 23. Juli 1998
This is the only book on numerical methods I can stand. But, not only can I stand it: now I love it. It's one of the cleverest books I ever met. Hamming must be a genius of insight. Even if you wrote your thesis on differential equations, I bet you will be enriched by reading his considerations on them, from the numerical precision viewpoint. The same is true for Fourier methods, only much more, as this is the main topic of this surprising and wonderful book. Since then I bought every book written by Hamming during his lifespan, which is unfortunately over.
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