Tài liệu Evaluation of Functions part 6 pptx

... it will look (in part) like this: f(x)=··· +[y 8 −α(8,x)y 9 −β(9,x)y 10 ]F 8 (x) +[y 7 −α(7,x)y 8 −β(8,x)y 9 ]F 7 (x) +[y 6 −α (6, x)y 7 −β(7,x)y 8 ]F 6 (x) +[y 5 −α(5,x)y 6 −β (6, x)y 7 ]F 5 (x) +··· +[y 2 −α(2,x)y 3 −β(3,x)y 4 ]F 2 (x) +[y 1 −α(1,x)y 2 −β(2,x)y 3 ]F 1 (x) +[c 0 +β(1,x)y 2 −β(1,x)y 2 ]F 0 (x) (5.5.22) Notice ... 2 of The Art of Computer Programming (Reading, MA: A...

Ngày tải lên: 24/12/2013, 12:16

... range of integration. { int j; float xr,xm,dx,s; static float x[]={0.0,0.1488743389,0.4333953941, The abscissas and weights. First value of each array not used. 0 .67 9409 568 2,0. 865 063 366 6,0.9739 065 285}; static ... used. 0 .67 9409 568 2,0. 865 063 366 6,0.9739 065 285}; static float w[]={0.0,0.2955242247,0. 269 266 7193, 0.2190 863 625,0.1494513491,0. 066 6713443}; xm=0.5*(b+a);...

Ngày tải lên: 15/12/2013, 04:15

... I.A. 1 964 , Handbook of Mathematical Functions , Applied Mathe- matics Series, Volume 55 (Washington: National Bureau of Standards; reprinted 1 968 by Dover Publications, New York), § 3 .6. Mathews, ... 1970, Mathematical Methods of Physics , 2nd ed. (Reading, MA: W.A. Benjamin/Addison-Wesley), § 2.3. [2] 5.2 Evaluation of Continued Fractions Continued fractions are often powerf...

Ngày tải lên: 15/12/2013, 04:15

... America). Thompson, I.J., and Barnett, A.R. 19 86, Journal of Computational Physics , vol. 64 , pp. 490–509. [5] Lentz, W.J. 19 76, Applied Optics , vol. 15, pp. 66 8 67 1. [6] Jones, W.B. 1973, in Pad´e Approximants ... generalizes to the evaluation of the polynomial and nd of its derivatives simultaneously: void ddpoly(float c[], int nc, float x, float pd[], int nd) Given the n...

Ngày tải lên: 15/12/2013, 04:15

... quadrature [1] . It is often combined with an adaptive choice of N, the number of Chebyshev coefficients calculated via equation (5.8.7), which is also the number of function evaluations of f(x). If a ... { cint[j]=con*(c[j-1]-c[j+1])/j; Equation (5.9.1). 1 96 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-52...

Ngày tải lên: 24/12/2013, 12:16

... ≡  y 2 (x) y 1 (x) G(x, y)dy (4 .6. 5) and finally our answer as an integral over H(x) I =  x 2 x 1 H(x)dx (4 .6. 6) In an implementation of equations (4 .6. 4)–(4 .6. 6), some basic one-dimensional integration ... [10] Kronrod, A.S. 1 964 , Doklady Akademii Nauk SSSR , vol. 154, pp. 283–2 86 (in Russian). [11] Patterson, T.N.L. 1 968 , Mathematics of Computation , vol. 22, pp. 847–8 56...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 15/12/2013, 04:15

... to make use of previous work: Terms like k! or (2k)! can be updated in a multiply or two. 165 166 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 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 evaluating funct...

Ngày tải lên: 15/12/2013, 04:15

... figures than evaluation of the Chebyshev sum directly (as by chebev). This is because the Chebyshev polynomials themselves exhibit a rather delicate cancellation: The leading coefficient of T n (x), ... figures less accuracy than the roundoff limit of your machine. You get the g’s in equation (5.10.1) from the c’s output from chebft (suitably truncated atamodest value of m)bycallingins...

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) ... using the coefficientof...

Ngày tải lên: 15/12/2013, 04:15