Tài liệu Evaluation of Functions part 12 doc

... Mathe- matical Association of America), pp. 59, 182–183 [synthetic division]. 5.11 Economization of Power Series One particular application of Chebyshev methods, the economization of power series,is an ... approximation in the interval of interest, by the methods of §5.8. We would have obtained just the same lower-order polynomial. The principal lesson is that the rate of conver...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 15/12/2013, 04:15

... large x. Accelerating the Convergence of Series There are several tricks for accelerating the rate of convergence of a series (or, equivalently, of a sequence of partial sums). These tricks will not ... America). Chapter 5. Evaluation of Functions 5.0 Introduction The purpose of this chapter is to acquaint you with a selection of the techniques that are frequently used in...

Ngày tải lên: 15/12/2013, 04:15

... the evaluation: double ratval(double x, double cof[], int mm, int kk) Given mm , kk ,and cof[0 mm+kk] , evaluate and return the rational function ( cof[0] + cof[1]x + ···+ cof[mm]x mm )/(1 + cof[mm+1]x + ... θ] sin(θ + δ)=sinθ−[αsin θ − β cos θ] (5.5.6) 176 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5...

Ngày tải lên: 24/12/2013, 12:16

... equations (5.7.4). This forces temp into and out of addressable memory. 188 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... early. } free_matrix(a,1,NTAB,1,NTAB); return ans; } In dfridr, the number of evaluationsof func is typically 6to 12, but isallowed to be as great as 2×NTAB. As a...

Ngày tải lên: 24/12/2013, 12:16

... execution time of chebft is dominated by the calculation of N 2 cosines, rather than by the N evaluations of your function, then you should look ahead to 12. 3, especially equation 12. 3.22, which ... an easy way of computing f(x) for all subsequent time. The first of these tasks is straightforward. A generalization of equation (5.8.7) that is here implemented is to allow the rang...

Ngày tải lên: 24/12/2013, 12:16

... h  23 12 f 2 + 7 12 f 3 + f 4 + f 5 + ···+f N−2 + 13 12 f N −1 + 5 12 f N  + O  1 N 3  (4.1.20) CITED REFERENCES AND FURTHER READING: Abramowitz, M., and Stegun, I.A. 1964, Handbook of Mathematical ... 136 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 ... fixed limits...

Ngày tải lên: 15/12/2013, 04:15

... trapzd, while qsimp requires 8 calls (8 times as many evaluations of the integrand) and qtrap requires 13 calls (making 256 times as many evaluations of the integrand). CITED REFERENCES AND FURTHER ... endpointsare also nonsingular. qromb, in such circumstances, takes many, many fewer function evaluations than either of the routines in §4.2. For example, the integral  2 0 x 4 log(x + ...

Ngày tải lên: 15/12/2013, 04:15

... it,j; b=sqrt(bb-aa); a=0.0; if (n == 1) { The rest of the routine is exactly like midpnt and is omitted. 142 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... double the number of steps in the extended midpoint rule and still have the benefit of previous function evaluations (try it!). However, it is possible to triple...

Ngày tải lên: 15/12/2013, 04:15

... Mathe- matical Association of America), pp. 59, 182–183 [synthetic division]. 5.11 Economization of Power Series One particular application of Chebyshev methods, the economization of power series,is an ... 198 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... than 10 −7 is x 13 /(2...

Ngày tải lên: 15/12/2013, 04:15