Tài liệu Integration of Functions part 7 pptx

... shape of the boundary of the region of integration simple or complicated? Inside the region, is the integrand smooth and simple, or complicated, or locally strongly peaked? Does 162 Chapter 4. Integration ... integration, plus a method of determining whether a random point is inside or outside the region of integration. Monte Carlo integration evaluates the function at a ran...

Ngày tải lên: 15/12/2013, 04:15

... (This particularchoiceis calledGauss-Chebyshevintegration, for reasons that will become clear shortly.) 156 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF ... range of integration. { int j; float xr,xm,dx,s; static float x[]={0.0,0.148 874 3389,0.4333953941, The abscissas and weights. First value of each array not used. 0. 679 4095682,0.8...

Ngày tải lên: 15/12/2013, 04:15

... 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

... Bernoulli numbers become very large, e.g., B 50 = 4950 572 05241 079 648212 477 525 66 The key point is that only even powers of h occur in the error series of (4.2.1). This fact is not, in general, shared ... 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Unsophisticated as it is, routine qtrap is in fact a fairly robust way of doi...

Ngày tải lên: 15/12/2013, 04:15

... 140 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... call 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). 4.3 Romberg Integration We can view Romberg’s method as the natural generalization of the routine qsimp ... the case of k...

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. 146 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... (4.1.19) shares with (4.1.11) the “deep” property 142 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC CO...

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 ... λa n+1 (5.2.11) leaves the value of a continued fraction unchanged. By a suitable choice of the scale factor λ you can often simplify the form of the a’s and...

Ngày tải lên: 15/12/2013, 04:15

... 490–509. [5] Lentz, W.J. 1 976 , Applied Optics , vol. 15, pp. 668– 671 . [6] Jones, W.B. 1 973 , in Pad´e Approximants and Their Applications , P.R. Graves-Morris, ed. (Lon- don: Academic Press), p. 125. [7] 5.3 Polynomials ... 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:...

Ngày tải lên: 15/12/2013, 04:15

... 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 ... relation is of little or no practical use in that direc...

Ngày tải lên: 24/12/2013, 12:16

... 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 ... hyperbolic function...

Ngày tải lên: 24/12/2013, 12:16