Preface to the First Edition XV linear equations (Chapter 2),interpolation and extrapolation(Chaper 3),integration (Chaper 4),nonlinear root-finding (Chapter 9),eigensystems (Chapter 11),and ordinary differential equations(Chapter 16).Most of these topics have been taken beyond their standard treatments into some advanced material which we have felt to be particularly important or useful. Some other subjects that we cover in detail are not usually found in the standard numerical analysis texts.These include the evaluation of functions and of particular special functions of higher mathematics(Chapters 5 and 6);random numbers and Monte Carlo methods (Chapter 7);sorting (Chapter 8);optimization,including multidimensional methods(Chapter 10);Fourier transform methods,including FFT methods and other spectral methods (Chapters 12 and 13);two chapters on the statistical description and modeling of data (Chapters 14 and 15);and two-point boundary value problems,both shooting and relaxation methods(Chapter 17). g The programs in this book are included in ANSI-standard C.Versions of the book in FORTRAN,Pascal,and BASIC are available separately.We have more to say about the c language,and the computational environment assumed by our routines.in $1.1 (Introduction). (Nort server Acknowledgments America computer, THE Many colleagues have been generous in giving us the benefit of their numerical and computational experience,in providing us with programs,in commenting on the manuscript,or in general encouragement.We particularly wish to thank George 9 Programs Rybicki,Douglas Eardley,Philip Marcus,Stuart Shapiro,Paul Horowitz,Bruce Musicus,Irwin Shapiro,Stephen Wolfram,Henry Abarbanel,Larry Smarr,Richard Muller,John Bahcall,and A.G.W.Cameron We also wish to acknowledge two individuals whom we have never met:Forman to dir Acton,whose 1970 textbook Numerical Methods that Work (New York:Harper and Row)has surely left its stylistic mark on us;and Donald Knuth,both for his series OF SCIENTIFIC COMPUTING (ISBN of books on The Art of Computer Programming(Reading,MA:Addison-Wesley), 1988-19920 and for TEX,the computer typesetting language which immensely aided production of this book. 10-621 Research by the authors on computational methods was supported in part by the U.S.National Science Foundation. Numerical Recipes 43108. October:1985 William H.Press Brian P.Flannery (outside 膜 Saul A.Teukolsky North oftware. William T.Vetterling AmerPreface to the First Edition xv Permission 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). linear equations (Chapter 2), interpolation and extrapolation (Chaper 3), integration (Chaper 4), nonlinear root-finding (Chapter 9), eigensystems (Chapter 11), and ordinary differential equations (Chapter 16). Most of these topics have been taken beyond their standard treatments into some advanced material which we have felt to be particularly important or useful. Some other subjects that we cover in detail are not usually found in the standard numerical analysis texts. These include the evaluation of functions and of particular special functions of higher mathematics (Chapters 5 and 6); random numbers and Monte Carlo methods (Chapter 7); sorting (Chapter 8); optimization, including multidimensional methods (Chapter 10); Fourier transform methods, including FFT methods and other spectral methods (Chapters 12 and 13); two chapters on the statistical description and modeling of data (Chapters 14 and 15); and two-point boundary value problems, both shooting and relaxation methods (Chapter 17). The programs in this book are included in ANSI-standard C. Versions of the book in FORTRAN, Pascal, and BASIC are available separately. We have more to say about the C language, and the computational environment assumed by our routines, in §1.1 (Introduction). Acknowledgments Many colleagues have been generous in giving us the benefit of their numerical and computational experience, in providing us with programs, in commenting on the manuscript, or in general encouragement. We particularly wish to thank George Rybicki, Douglas Eardley, Philip Marcus, Stuart Shapiro, Paul Horowitz, Bruce Musicus, Irwin Shapiro, Stephen Wolfram, Henry Abarbanel, Larry Smarr, Richard Muller, John Bahcall, and A.G.W. Cameron. We also wish to acknowledge two individuals whom we have never met: Forman Acton, whose 1970 textbook Numerical Methods that Work (New York: Harper and Row) has surely left its stylistic mark on us; and Donald Knuth, both for his series of books on The Art of Computer Programming (Reading, MA: Addison-Wesley), and for TEX, the computer typesetting language which immensely aided production of this book. Research by the authors on computational methods was supported in part by the U.S. National Science Foundation. October, 1985 William H. Press Brian P. Flannery Saul A. Teukolsky William T. Vetterling