Numerical Recipes in Fortran 77: The Art of Scientific Computing 2nd Edition by William H. Press (PDF)

Description

This is the greatly revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, this new edition remains the most practical, comprehensive handbook of scientific computing available today. Highlights of the new material include: -A new chapter on integral equations and inverse methods -Multigrid and other methods for solving partial differential equations -Improved random number routines – Wavelet transforms -The statistical bootstrap method -A new chapter on “less-numerical” algorithms including compression coding and arbitrary precision arithmetic. The book retains the informal easy-to-read style that made the first edition so popular, while introducing some more advanced topics. It is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. The Second Edition is availabe in FORTRAN, the traditional language for numerical calculations and in the increasingly popular C language.

User’s Reviews

Editorial Reviews: Review “This is a phenomenal effort. Virtualy anyone involved in scientific computing, from engineers, to physicists, to social scientists, will find information and methods applicable to their specific needs, or helpful subroutines that can be inserted into the reader’s existing programs….No matter what language you program in, these packages are classics, both as a textbook or reference. They are an essential and valuable addition to the academic, professional, or personal library.” Internet”Anyone who writes (or is curious about) computer codes to solve many of the common numerical problems in science and engineering will want to own this large book. The writing is authoritative (two of the authors have published first-rate research in writing code for astrophysics problems), but never dull. Flashes of humor appear at regular intervals, in the appropriate places, and as hard as it may be to believe, this book is interesting even as casual reading! I recommend this book highly, and both the authors and the publisher are to be commended for an outstanding piece of work.” Paul J. Nahin, Science Books and Films”This encyclopedic book should be read (or at least owned) not only by those who must roll their own numerical methods, but by all who must use prepackaged programs.” Mike Holderness, New Scientist”This reviewer knows of no other single source of so much material of this nature. Highly recommended.” R.J. Wernick, Choice”…will be appreciated by anyone involved in the numerical solution of engineering problems….the authors have successfully blended tutorial discussion, fundamental mathematics, explanation of algorithms, and working computer programs into neatly packaged chapters covering all of the basic topics in numerical methods. What sets this book apart, in the reviewer’s opinion, is the versatility of the book….indispensable.” Ben H. Thacker, Applied Mechanics Review”If you already have the first edition, will you want or need the second? The answer is a definitive yes….a book that should be on your desk (not your shelf) if you have any interest in the analysis of data or the formulation of models….The second edition contains numerous additions of important material, such as a section on Cholesky decomposition (which is critical for simulating multivariate distributions), discussion of the bootstrap method, and the addition and expansion of other numerical methods too numerous to mention here.” Lyle W. Konigsberg, Human Biology”…a valuable resource for those with a specific need for numerical software. The routines are prefaced with lucid, self-contained explanations….highly recommended for those who require the use and understanding of numerical software.” Elizabeth Greenwell Yanik, SIAM Review”…the second [edition] expands the scope of coverage and continues the standard of excellence achieved in the first. If you were to have only a single book on numerical methods, this is the one I would recommend.” Edmund Miller, IEEE Computational Science & Engineering Book Description This is the revised and expanded second edition of the hugely popular Numerical Recipes: the Art of Scientific Computing. From the Back Cover This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on “less-numerical” algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic topics as: linear equations, interpolation and extrapolation, integration, nonlinear root-finding, eigensystems, ordinary differential equations, evaluation of functions, sorting, optimization, statistical description and modeling of data, and two-point boundary value problems. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am a scientist who does a lot of numerical analysis. I have been using a lot of commercial apps (e.g. Excel) as well as a lot of high-level interpreted languages to do my work. However, I recently discovered that these packages were actually returning the wrong answers. This is because of how variables have to be reset and other software requirements which, frankly, I would have never discovered if I hadn’t had some colleagues who were CSE majors.So I binned the packages, downloaded a FORTRAN compiler for about $200, and wrote my own code. But to save myself a lot of trouble I turned to this book that I had used in graduate school. All of the routines are there – matrix operations, transforms, numerical integration – and shortly I was back to crunching data.Why FORTRAN? First, it’s sort of the Latin of scientific computing. It might be old but there is a lot of legacy code (as evidenced by this book) that has been tested over and over. Second, it is incredibly easy to write. Third, you KNOW what it is doing, you’re not trusting some algorithm written by somebody else who wasn’t trying to solve the problem you’re trying to solve. And this code runs quickly. Data analysis that took two to three minutes in Excel takes a few seconds with these programs and subroutines.It’s like driving a car with a manual transmission – once you get the hang of it you have a great deal more control and can make your code go like you want it. And so much of that code is right here, waiting for you.

⭐This perhaps the best resource available for scientific programming. It is filled with code samples and mathematical theory. The book assumes a thorough knowledge of mathematics and physics as well as good skills in writing fortran code. Since the book contains only pseudocode, the “recipes” are applicable to all FORTRAN standards (except FORTRAN IV through 60). Time to let go of Hollerith numbers.

⭐It gives a good description of numerical algorithms. What interested me with the discussion of Lanczos coeffiecients to evaluate the gamma function was that the solutions are not unique and a different set of coefficients might be found which makes the algorithm more efficient. They don’t mention that in the book. Maybe this applies to other algorithms in the book?

⭐I used Fortran for 30 plus years and adapted to Object Oriented languages for the final 15 years of my career. I purchased this book for a Lagrangian interpolation routine which I quickly converted. Has many code examples which I am sure I will draw from again.

⭐Written for FORTRAN but also bought C version great solution book for implementation of numerical methods in systems that do not have advanced mathematical libraries

⭐Out of date now – you need the latest versions

⭐classics

⭐Like everybody else here, I first learnt Fortran so I know how relevant still is. It always goes first on the section “Computer Languages” of my CV.Back in my Computation Methods course, we were only required to learn to write Fortran code for matrix multiplication, run a FFT and that was all. Because of my current goals, I’m doing a deep dive in the next item: LU factorization of a matrix A = LU, to later find its inverse A^-1…Matlab, python, etc have built in LU factorizations tools, but I want to know how it worksI was checking online resources first but had some lingering unanswered questions: where do I store the ones of the main diagonal in the L matrix? The matrix A is said to be replaced by the calculated values of L and U but does that mean that you still need to create additional memory space for the matrix U? Why we do pivoting on the rows but not in the columns? How do I do bookkeeping of the permutations of the rows?Was I supposed to figure those questions by my own from the online resources ? Perhaps, but re-reads of them didn’t answer those.No problem, Numerical Recipes addressed those questions and explained them explicitly: the ones of the main diagonal of L are never stored, and you don’t actually allocate new memory for the U matrix, the values of **both** L and U are stored in the corresponding file-column location of A, that’s why A gets “destroyed’. Column pivoting would make the code too complex and unpractical. You do bookkeeping of the row permutations using an auxiliary array of plus and minus ones…long story short: Thank you Numerical Recipes!The casual style of the authors is also most welcomed as wellIf I was an instructor, I would ask students to read the book as supplementary material…but in my case is main material…Even if you write in contemporary languages like Python, R, Julia, etc…the explanations of NR are timeless and continue being relevant across multiple scripting softwares

⭐The go-to book for numerical methods. The code is great, well-tested and easy to use, and easy to adapt to e.g. F90, but one of the most useful things about the big thick volume is the description of the methods, especially the stats. If you haven’t got a (very) well-thumbed version of numerical recipes in your language of preference you can’t call yourself a numericist in any discipline.

⭐This book features about every numerical standard algorithm you will ever need to do scientific, performant computing in fortran. I use it to get an idea to code in C++, and this book is totally worth it (in contrast to the C++ version of it, which is just bad).If you do numerical calculations on a daily basis, you should read this book!

⭐No coloured pictures, no funny stories … just packed with recipes. Some programs may need reediting to suit to you own compiler.

⭐This is an excellent book, contains ‘tons’ of hardworking, it is beautiful!

⭐一時代前のデータ処理の実務書だが，データについての考え方を，今のデータ・クラウドの時代に照らして，再検討するいい材料になる。

⭐

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