Tài liệu Evaluation of Functions part 10 pptx

... 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 ... routine chebft §5.8,andgiven n , the desired degree of approximation (length of c to be used), this routine returns the array cder[0 n-1] ,the Chebyshev coefficients of the...

Ngày tải lên: 24/12/2013, 12:16

... precision, say 10 −7 or 10 −15 . The parameter tiny should be less than typical values of eps|b j |,say10 −30 . The above algorithm assumes that you can terminate the evaluation of the continued ... 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

... the evaluation: double ratval(double x, double cof[], int mm, int kk) Given mm , kk ,and cof[0 mm+kk] , evaluate and return the rational function ( cof[0] + cof[1]x + ···+ cof[mm]x mm )/(1 + cof[mm+1]x + ... (j=nv;j<=n;j++) r[j]=0.0; } 176 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4 3108 -5) Copyright (...

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... combination of J 0 and J 1 , which are of order unity. 180 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4 3108 -5) Copyright ... ± √ b 2 − 4ac 2a (5.6.2) 182 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4 3108 -5) Copyright (...

Ngày tải lên: 24/12/2013, 12:16

... polynomial of one lower order. z1=z; z=z1-p1/pp; Newton’s formula. 156 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4 3108 -5) Copyright ... i.e., the computation of the coefficients a j , b j in (4.5.6); (ii) the determination of the zeros of p N (x),and the computation of the associated weights. For t...

Ngày tải lên: 15/12/2013, 04:15

... York: Wiley), §§ 2.9–2 .10. Ralston, A., and Rabinowitz, P. 1978, 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 ... 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 n...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 15/12/2013, 04:15

... large x. Accelerating the Convergence of Series There are several tricks for accelerating the rate of convergence of a series (or, equivalently, of a sequence of partial sums). These tricks will not ... America). Chapter 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...

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... 198 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4 3108 -5) Copyright (C) 1988-1992 by Cambridge ... 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 ....

Ngày tải lên: 15/12/2013, 04:15

... 200 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4 3108 -5) Copyright (C) 1988-1992 by Cambridge ... be. chebpc(c,d,NFEW); pcshft(a,b,d,NFEW); In our example, by the way, the 8th through 10th Chebyshev coefficients turn out to be on the order of −7 × 10 −6 , 3 × 10 −7 ,and−9 10 −9 , so reasonable truncati...

Ngày tải lên: 15/12/2013, 04:15