Tài liệu Evaluation of Functions part 7 ppt

... McGraw-Hill), § 6.1. McKelvey, J.P. 1984, American Journal of Physics , vol. 52, pp. 269– 270 ; see also vol. 53, p. 77 5, and vol. 55, pp. 374 – 375 . ... Li- brary), p. 76 . 5.6 Quadratic and Cubic Equations The roots of simple algebraic equations can be viewed as being functions of the equations’ coefficients. We are taught these functions in elementary ... b, c, namely x = −b...

Ngày tải lên: 24/12/2013, 12:16

... A., and Rabinowitz, P. 1 978 , A First Course in Numerical Analysis , 2nd ed. (New York: McGraw-Hill), §§ 4.4–4.8. 4.6 Multidimensional Integrals Integrals of functions of several variables, over ... the number of function evaluations needed to sample an N-dimensional space increases as the Nth power of the number needed to do a one-dimensional integral. If you need 30 function eval...

Ngày tải lên: 15/12/2013, 04:15

... necessarily including the domain of convergence of the series, however). Sometimes the continued fraction converges best where the series does worst, although this is not 170 Chapter 5. Evaluation of Functions Sample ... MA: W.A. Benjamin/Addison-Wesley), § 2.3. [2] 5.2 Evaluation of Continued Fractions Continued fractions are often powerful ways of evaluating functions th...

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... simultaneously: p=c[n]; dp=0.0; for(j=n-1;j>=0;j ) {dp=dp*x+p; p=p*x+c[j];} 174 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... 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) Giv...

Ngày tải lên: 15/12/2013, 04:15

... the first five terms in the power series expansion of an unknown function f(x), f(x) ≈ 2+ 1 9 x+ 1 81 x 2 − 49 874 8 x 3 + 175 78 732 x 4 + ··· (5.12 .7) (It is not really necessary that you know the ... to the same function, namely ( cof[0] + cof[1] x + ···+ cof[n] x N )/(1 + cof[n+1] x + ···+ 5.12 Pad´e Approximants 203 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC CO...

Ngày tải lên: 24/12/2013, 12:16

... evaluated, i.e., fineness of the mesh.bb=dvector(1,npt); coff=dvector(0,ncof-1); ee=dvector(1,npt); fs=dvector(1,npt); u=dmatrix(1,npt,1,ncof); v=dmatrix(1,ncof,1,ncof); w=dvector(1,ncof); wt=dvector(1,npt); 5.13 ... **v); These are double versions of svdcmp, svbksb. int i,it,j,ncof,npt; double devmax,e,hth,power,sum,*bb,*coff,*ee,*fs,**u,**v,*w,*wt,*xs; ncof=mm+kk+1; npt=NPFAC*ncof; Numbe...

Ngày tải lên: 24/12/2013, 12:16

... wish to keep open the possibility of altering this choice for some applications. Our golden brick consists of a collection of routines for the integration of sets of ordinary differential equations, ... > 1. An implementation of this algorithm is given in §6.12 as the routine hypgeo. 210 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART...

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... 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 ... 178 Chapter 5. Evaluation of Functions Sample page...

Ngày tải lên: 24/12/2013, 12:16

... 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 ... degree of approximation (length of c to be used), this routine returns the array cint[0 n-1] ,the Chebyshev coefficients of the integral of the function whose coefficients are c...

Ngày tải lên: 24/12/2013, 12:16

... Science vol. 1, pp. 54 77 . [2] Avni, Y. 1 976 , Astrophysical Journal , vol. 210, pp. 642–646. [3] Lampton, M., Margon, M., and Bowyer, S. 1 976 , Astrophysical Journal , vol. 208, pp. 177 –190. Brownlee, ... even when they must be offered without proof. Figure 15.6.1 shows the conceptual scheme of an experiment that “measures” a set of parameters. There is some underlying true set of...

Ngày tải lên: 15/12/2013, 04:15