Tài liệu Integration of Functions part 6 pptx

... 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

... ≡  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 routine ... 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 str...

Ngày tải lên: 15/12/2013, 04:15

... 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

... 1 36 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... READING: Abramowitz, M., and Stegun, 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 ... even values (o...

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) ... North America). 4.3 Romberg Integration We can view Romberg’s method as the natural generalization of the routine qsimp in the last section to integration schemes that are of higher order than Simpson’s ... total number of st...

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. 1 46 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... answer; answer=qromo(bessy0,0.0,2.0,midpnt); 144 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COM...

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 powerful...

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 ... 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 nc+1 coefficients o...

Ngày tải lên: 15/12/2013, 04:15

... 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 . The constant of integration ... the constant of integration. fac = -fac; Will equal ±1. } cint[n-1]=con*c[n-2]/(n-1); Special case of (5.9.1) for n-1. sum += fac*cint[n-1]; cint[0]=2.0*sum; Set the con...

Ngày tải lên: 24/12/2013, 12:16

... members of a set of vectors, they are said to be a conjugate set. If you do successive line minimization of a function along a conjugate set of directions, then you don’t need to redo any of those ... in your application,calculation of the gradient is out of the question. You might first think of this simple method: Take the unit vectors e 1 , e 2 , e N as a setofdirections.Usi...

Ngày tải lên: 15/12/2013, 04:15