Numerical Recipes in FORTRAN 90: The Art of Parallel Scientific Computing (FORTRAN Numerical Recipes, Volume 2)

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.--book Jacket. Preliminaries; Solution Of Linear Algebraic Equations; Interpolation And Extrapolation; Integration Of Functions; Evaluation Of Functions; Special Functions; Random Numbers; Sorting; Root Finding And Nonlinear Sets Of Equations; Minimization Or Maximization Of Functions; Eigensystems; Fast Fourier Transform; Fourier And Spectral Applications; Statistical Description Of Data; Modeling Of Data; Integration Of Ordinary Differential Equations; Two Point Boundary Value Problems; Integral Equations And Inverse Theory; Partial Differential Equations; Less-numerical Algorithms; Index Of Programs And Dependencies. William H. Press ... [et Al.]. Includes Bibliographical References (p. 916-919) And Index. Contents......Page 5 Preface to Volume 2......Page 8 Foreword......Page 10 License Information......Page 17 21.0 Introduction......Page 21 21.1 Quick Start: Using the Fortran 90 Numerical Recipes Routines......Page 22 21.2 Fortran 90 Language Concepts......Page 23 21.3 More on Arrays and Array Sections......Page 27 21.4 Fortran 90 Intrinsic Procedures......Page 31 21.5 Advanced Fortran 90 Topics......Page 39 21.6 And Coming Soon: Fortran 95......Page 45 22.0 Why Think Parallel?......Page 48 22.1 Fortran 90 Data Parallelism: Arrays and Intrinsics......Page 50 22.2 Linear Recurrence and Related Calculations......Page 57 22.3 Parallel Synthetic Division and Related Algorithms......Page 63 22.4 Fast Fourier Transforms......Page 67 22.5 Missing Language Features......Page 69 23.0 Introduction and Summary Listing......Page 73 23.1 Routines That Move Data......Page 76 23.2 Routines Returning a Location......Page 78 23.3 Argument Checking and Error Handling......Page 80 23.4 Routines for Polynomials and Recurrences......Page 82 23.5 Routines for Outer Operations on Vectors......Page 86 23.6 Routines for Scatter with Combine......Page 88 23.7 Routines for Skew Operations on Matrices......Page 90 23.8 Other Routine(s)......Page 93 Fortran 90 Code Chapters B1–B20......Page 95 B1. Preliminaries......Page 96 B2. Solution of Linear Algebraic Equations......Page 100 B3. Interpolation and Extrapolation......Page 129 B4. Integration of Functions......Page 138 B5. Evaluation of Functions......Page 156 B6. Special Functions......Page 169 B7. Random Numbers......Page 227 B8. Sorting......Page 253 B9. Root Finding and Nonlinear Sets of Equations......Page 268 B10. Minimization or Maximization of Functions......Page 287 B11. Eigensystems......Page 311 B12. Fast Fourier Transform......Page 321 B13. Fourier and Spectral Applications......Page 339 B14. Statistical Description of Data......Page 355 B15. Modeling of Data......Page 371 B16. Integration of Ordinary Differential Equations......Page 383 B17. Two Point Boundary Value Problems......Page 400 B18. Integral Equations and Inverse Theory......Page 411 B19. Partial Differential Equations......Page 418 B20. Less-Numerical Algorithms......Page 429 References......Page 445 C1.1 Numerical Recipes Types (nrtype)......Page 447 C1.2 Numerical Recipes Utilities (nrutil)......Page 450 C2. Alphabetical Listing of Explicit Interfaces......Page 470 C3. Index of Programs and Dependencies......Page 520 General Index to Volumes 1 and 2......Page 533 Numerical Recipes in Fortran 90 starts with a detailed introduction to the Fortran 90 language and then presents the basic concepts of parallel programming. All 350+ routines from the second edition of Numerical Recipes are presented in Fortran 90. Many are completely reworked algorithmically so as to be 'parallel-ready' and to utilise Fortran 90's advanced language features. Numerical Recipes in Fortran 90 emphasises general principles, but throughout there are also numerous hints and tips. This volume is intended for use with the original Numerical Recipes in Fortran, 2nd Edition (now called Numerical Recipes in Fortran 77) and does not discuss how the individual programs are used, or how the mathematical methods are used. An excellent guide for Fortran programmers interested in moving to Fortran 90, or C/C++ programmers interested in parallel programming. New text with detailed F 90 tutorial and introduction to parallel programming All routines from the second edition of Numerical Recipes are presented in Fortran 90, many reworked to be 'parallel-ready' ([source][1]) [1]: https://www.cambridge.org/nl/academic/subjects/mathematics/numerical-recipes/numerical-recipes-fortran-90-art-parallel-scientific-computing-volume-2-2nd-edition?format=HB&isbn=9780521574396 1. Introduction to Fortran 90 language features 2. Introduction to parallel programming 3. Numerical recipes utility functions for Fortran 90 Part I. Fortran 90 Code chapters: 4. Preliminaries 5. Solution of linear algebraic equations 6. Interpolation and extrapolation 7. Integration of functions 8. Evaluation of functions 9. Special functions 10. Random numbers 11. Sorting 12. Root finding and nonlinear sets of equations 13. Minimization or maximization of functions 14. Eigensystems 15. Fast Fourier transform 16. Fourier and spectral applications 17. Statistical description of Data 18. Modelling of data 19. Integration of ordinary differential equations 20. Two point boundary value problems 21. Integral equations and inverse theory 22. Partial differential equations 23 Less-numerical algorithms Part II. Appendices: 24. Listing of utility modules (nrtype and nrutil) 25. Listing of explicit interfaces 26. Index of programs and dependencies. This is a complete guide for learning how to "think parallel". The treatment emphasizes general principles, but sprinkled throughout are also numerous "parallel hints" and "Fortran 90 tips". The Fortran 90 language is not just the long-awaited updating of Fortran to modern computing practices--it is the cutting edge of the multiprocessor computers and widespread parallel programming. The newest product in the hugely popular Numerical Recipes series, Numerical Recipes in Fortran 90 has three completely new chapters that start with a detailed introduction to the Fortran 90 language and then present the basic concepts of parallel programming with the same clarity and cheer for which Numerical Recipes is famous. Fortran 90 is in many respects a backwards-compatible modernization of the long-used (and much abused) Fortran 77 language, but it is also, in other respects, a new language for parallel programming on present and future multiprocessor machines. v. 1. Numerical recipes in FORTRAN 77 : the art of scientific computing v. 2. Numerical recipes in FORTRAN 90 : the art of parallel scientific computing.