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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call North America only),or send email to [email protected] (outside North America).. Barnett, A.R., Feng, D.H., Steed, J.W., and Goldfarb, L.J.B. 1974, Computer Physics Commu- nications...
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The most convenient way of evaluating these functions to arbitrary precision is to use power series for small x and a continued fraction for large x. There is a complex continued fraction that yields both S(x) and C(x) si- multaneously:. In the last line we have converted the “standard” form of the continued fraction to its “even” form (see §...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call North America only),or send email to [email protected] (outside...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Only a few of the standard books on numerical methods [3-4] treat topics relating to random numbers.. 2 of The Art of Computer Programming (Reading, MA: Addison-Wesley), Chapter 3, especially § 3.5. Bratley, P., Fox,...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. In the previous section, we learned how to generate random deviates with a uniform probability distribution, so that the probability of generating a number between x and x + dx, denoted p(x)dx, is given by....
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2 of The Art of Computer Programming (Reading, MA: Addison-Wesley), pp. 7.3 Rejection Method: Gamma, Poisson, Binomial Deviates. The rejection method is a powerful, general technique for generating random deviates whose distribution function p(x)dx (probability of a value occurring between x and x + dx) is known and computable. The rejection method does not require that the cumulative distribution function...
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Of course you can just generate uniform random deviates between zero and one and use their high-order bit (i.e., test if they are greater than or less than 0.5). One method for generating random bits, with two variant implementations, is based on “primitive polynomials modulo 2.” The theory of these polynomials is beyond our scope (although § 7.7 and §...
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(We chose 18 because 2 18 is small enough for you to verify our claims directly by numerical experiment.) The accompanying table [2] lists one primitive polynomial for each degree up to 100. 2 of The Art of Computer Programming (Reading, MA: Addison-Wesley), pp. Meyer and Matyas [4] discuss the importance of the cipher function being nonlinear, as well as...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Validating the Correctness of Hardware Implementations of the NBS Data Encryption Standard , 1980, NBS Special Publication 500–20 (Washington: U.S. 3 of The Art of Computer Programming (Reading, MA: Addison-Wesley), Chapter 6. Vitter, J.S., and...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Hammersley, J.M., and Handscomb, D.C. 1964, Monte Carlo Methods (London: Methuen).. (ed.) 1966, The Monte Carlo Method (Oxford: Pergamon).. 1974, The Monte Carlo Method (Chicago: University of Chicago Press).. Kalos, M.H., and Whitlock, P.A. 1986,...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. 7.8 Adaptive and Recursive Monte Carlo Methods. This section discusses more advanced techniques of Monte Carlo integration. As examples of the use of these techniques, we include two rather different, fairly sophisticated, multidimensional Monte Carlo...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call North America only),or send email to [email protected] (outside North America).. This chapter almost doesn’t belong in a book on numerical methods. However, some practical...
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20, roughly, the method of straight insertion. 3 of The Art of Computer Programming (Reading, MA: Addison-Wesley). 8.1 Straight Insertion and Shell’s Method. Sorts an array arr[1..n] into ascending numerical order, by straight insertion. 8.1 Straight Insertion and Shell’s Method 331. Sorts an array arr[1..n] into ascending numerical order, by straight insertion, while making the corresponding rearrangement of the array...
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3 of The Art of Computer Programming (Reading, MA: Addison-Wesley. It is a “partition-exchange” sorting method: A “partitioning element” a is selected from the array. The partitioning process is carried out by selecting some element, say the leftmost, as the partitioning element a . a, and then scan another pointer down from the end of the array until you find...
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1978, Communications of the ACM , vol. Definition (8.3.1) will make sense if you think of the numbers a i as being arranged in a binary tree, with the top, “boss,”. (See Figure 8.3.1.) In this form, a heap has every “supervisor” greater than or equal to its two “supervisees,” down through the levels of the hierarchy.. If you have...
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Instead, one can construct an index table I j , j = 1. void indexx(unsigned long n, float arr. unsigned long indx[]). i.e., outputs the array indx[1..n] such that arr[indx[j]] is in ascending order for j = 1, 2. unsigned long i,indxt,ir=n,itemp,j,k,l=1;. index table. void sort3(unsigned long n, float ra. An index table is constructed via the routine indexx. unsigned...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. rank of the jth element of the original array of keys, ranging from 1 (if that element was the smallest) to N (if that element was the largest). void rank(unsigned long n, unsigned long indx....
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3 of The Art of Computer Programming (Reading, MA: Addison-Wesley).. For example, you may have a list of facts like: “Element 3 and element 7 are in the same class;. element 19 and element 4 are in the same class. element 7 and element 12 are in the same class. Alternatively, you may have a procedure, given the numbers of...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. Simultaneous solution of equations in N dimensions is much more difficult than finding roots in the one-dimensional case. Hamming’s motto, “the purpose of computing is insight, not numbers,” is particularly apt in the area of...
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Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN Copyright (C by Cambridge University Press.Programs Copyright (C by Numerical Recipes Software. We will say that a root is bracketed in the interval (a, b) if f(a) and f (b) have opposite signs. If the function is continuous, then at least one root must lie in that...