Preface to the Second Edition Our aim in writing the original edition of Numerical Recipes was to provide a book that combined general discussion,analytical mathematics,algorithmics,and actual working programs.The success of the first edition puts us now in a difficult, though hardly unenviable,position.We wanted,then and now,to write a book that is informal.fearlessly editorial.unesoteric.and above all useful.There is a danger that,if we are not careful,we might produce a second edition that is weighty, balanced,scholarly,and boring. It is a mixed blessing that we know more now than we did six years ago.Then, we were making educated guesses,based on existing literature and our own research, about which numerical techniques were the most important and robust.Now.we have the benefit of direct feedback from a large reader community.Letters to our alter-ego enterprise,Numerical Recipes Software,are in the thousands per year.(Please,don't telephone us.Our post office box has become a magnet for letters pointing out that we have omitted some particular technique,well known to be important in a particular field of science or engineering.We value such letters,and digest them carefully,especially when they point us to specific references in the literature. 三多 The inevitable result of this input is that this Second Edition of Numerical Recipes is substantially larger than its predecessor,in fact about 50%larger both in 9苏 words and number of included programs(the latter now numbering well over 300). "Don't let the book grow in size,"is the advice that we received from several wise colleagues.We have tried to follow the intended spirit of that advice,even as we g violate the letter of it.We have not lengthened,or increased in difficulty,the book's principal discussions of mainstream topics.Many new topics are presented at this same accessible level.Some topics,both from the earlier edition and new to this one,are now set in smaller type that labels them as being"advanced."The reader 6 who ignores such advanced sections completely will not,we think.find any lack of continuity in the shorter volume that results. 92y Here are some highlights of the new material in this Second Edition .a new chapter on integral equations and inverse methods a detailed treatment of multigrid methods for solving elliptic partial differential equations routines for band diagonal linear systems ecipes .improved routines for linear algebra on sparse matrices .Cholesky and OR decomposition (outside orthogonal polynomials and Gaussian quadratures for arbitrary weight North Software. functions methods for calculating numerical derivatives Pade approximants,and rational Chebyshev approximation America). Bessel functions,and modified Bessel functions,of fractional order;and several other new special functions improved random number routines quasi-random sequences routines for adaptive and recursive Monte Carlo integration in high- dimensional spaces globally convergent methods for sets of nonlinear equations XiPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). Preface to the Second Edition Our aim in writing the original edition of Numerical Recipes was to provide a book that combined general discussion, analytical mathematics, algorithmics, and actual working programs. The success of the first edition puts us now in a difficult, though hardly unenviable, position. We wanted, then and now, to write a book that is informal, fearlessly editorial, unesoteric, and above all useful. There is a danger that, if we are not careful, we might produce a second edition that is weighty, balanced, scholarly, and boring. It is a mixed blessing that we know more now than we did six years ago. Then, we were making educated guesses, based on existing literature and our own research, about which numerical techniques were the most important and robust. Now, we have the benefit of direct feedback from a large reader community. Letters to our alter-ego enterprise, Numerical Recipes Software, are in the thousands per year. (Please, don’t telephone us.) Our post office box has become a magnet for letters pointing out that we have omitted some particular technique, well known to be important in a particular field of science or engineering. We value such letters, and digest them carefully, especially when they point us to specific references in the literature. The inevitable result of this input is that this Second Edition of Numerical Recipes is substantially larger than its predecessor, in fact about 50% larger both in words and number of included programs (the latter now numbering well over 300). “Don’t let the book grow in size,” is the advice that we received from several wise colleagues. We have tried to follow the intended spirit of that advice, even as we violate the letter of it. We have not lengthened, or increased in difficulty, the book’s principal discussions of mainstream topics. Many new topics are presented at this same accessible level. Some topics, both from the earlier edition and new to this one, are now set in smaller type that labels them as being “advanced.” The reader who ignores such advanced sections completely will not, we think, find any lack of continuity in the shorter volume that results. Here are some highlights of the new material in this Second Edition: • a new chapter on integral equations and inverse methods • a detailed treatment of multigrid methods for solving elliptic partial differential equations • routines for band diagonal linear systems • improved routines for linear algebra on sparse matrices • Cholesky and QR decomposition • orthogonal polynomials and Gaussian quadratures for arbitrary weight functions • methods for calculating numerical derivatives • Pade approximants, and rational Chebyshev approximation ´ • Bessel functions, and modified Bessel functions, of fractional order; and several other new special functions • improved random number routines • quasi-random sequences • routines for adaptive and recursive Monte Carlo integration in high￾dimensional spaces • globally convergent methods for sets of nonlinear equations xi