Tài liệu Integration of Functions part 4 docx

... 140 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1988-1992 by ... 1-800-872- 742 3 (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...

Ngày tải lên: 15/12/2013, 04:15

... formulas of higher order for this situation, but we will refrain from giving them. The semi-open formulas arejusttheobviouscombinations ofequations (4. 1.11)– (4. 1. 14) with (4. 1.15)– (4. 1.18), respectively. ... combination S = 4 3 S 2N − 1 3 S N (4. 2 .4) will cancel out the leading order error term. But there is no error term of order 1/N 3 , by (4. 2.1). The surviving error is...

Ngày tải lên: 15/12/2013, 04:15

... (b>a) (4. 4 .4) If there is a singularity at both limits, divide the integral at an interior breakpoint as in the example above. Equations (4. 4.3) and (4. 4 .4) are particularly simple in the case of ... 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 COMPUTING (ISBN 0-521 -43 108-5)...

Ngày tải lên: 15/12/2013, 04:15

... 1-800-872- 742 3 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). #include <math.h> #define EPS 3.0e- 14 Relative precision. #define PIM4 0.751125 544 4 649 425 1/π 1 /4 . #define ... used. 0.67 940 95682,0.8650633666,0.9739065285}; static float w[]={0.0,0.2955 242 247 ,0.2692667193, 0.2190863625,0. 149 451 349 1,0.066671 344 3}; xm=0.5*(b+a); xr=0.5...

Ngày tải lên: 15/12/2013, 04:15

... 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 regions with dimension greater than one, ... ≡  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 bas...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 15/12/2013, 04:15

... simultaneously: p=c[n]; dp=0.0; for(j=n-1;j>=0;j ) {dp=dp*x+p; p=p*x+c[j];} 1 74 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1988-1992 by ... be precomputed by A =(a 4 ) 1 /4 B= a 3 −A 3 4A 3 D=3B 2 +8B 3 + a 1 A−2a 2 B A 2 C = a 2 A 2 −2B−6B 2 −D E =a 0 −B 4 −B 2 (C+D)−CD (5.3....

Ngày tải lên: 15/12/2013, 04:15

... 5.8.1), T 0 (x)=1 T 1 (x)=x T 2 (x)=2x 2 −1 T 3 (x)=4x 3 −3x T 4 (x)=8x 4 −8x 2 +1 ··· T n+1 (x)=2xT n (x)− T n−1 (x) n ≥ 1. (5.8.2) (There also exist inverse formulas for the powers of x in terms of the T n ’s — see equations ... 190 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1...

Ngày tải lên: 24/12/2013, 12:16

... "IP lmsg .= "M ail($email, ("<p>Thôn ạn thành côn ồng hồ trên de: HP e_offset ="0 = ($time _of e = date(" h "$time"; ạn thành côn thông tin U 1 file logge bạn ... default '', `comments` text NOT NULL, `date` timestamp( 14) NOT NULL, PRIMARY KEY (`id`), ) TYPE=MyISAM AUTO_INCREMENT =41 9 ; B2:Viết 1 file config.php có nội dung...

Ngày tải lên: 15/12/2013, 01:16

... considerations of the previous section more meaningful. We consider the problem of fitting a set of N data points (x i ,y i )to a straight-line model y(x)=y(x;a, b)=a+bx (15.2.1) 662 Chapter 15. Modeling of ... uncertainty in the determination of those parameters. If the data are independent, then each contributes its own bit of uncertainty to the parameters. Consideration of pro...

Ngày tải lên: 15/12/2013, 04:15