Tài liệu Evaluation of Functions part 15 ppt

... 1964, Handbook of Mathematical Functions , Applied Mathe- matics Series, Volume 55 (Washington: National Bureau of Standards; reprinted 1968 by Dover Publications, New York). [1] 5.14 Evaluation of Functions ... can also be applied to other special functions. For 5.14 Evaluation of Functions by Path Integration 211 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIEN...

Ngày tải lên: 24/12/2013, 12:16

... 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 ways of evaluating functions ... 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...

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 + ... think, because software companies assign inexperienced programmers to what they believe to be the perfectly trivial task of implementing complex arithmetic. 174 Chapter 5. Evaluation...

Ngày tải lên: 15/12/2013, 04:15

... 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 COMPUTING (ISBN ... T n+1 , which itself has n +2extrema of equal magnitude and alternating sign. So, here, the number of rational coefficients, m + k +1, plays the same role of the number of polynomial...

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); 208 Chapter ... **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...

Ngày tải lên: 24/12/2013, 12:16

... a canceling linear 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 ... b, c, namely x = −b ± √ 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 0-521-43108-5) C...

Ngày tải lên: 24/12/2013, 12:16

... Journal of Physics , vol. 52, pp. 269–270; see also vol. 53, p. 775, and vol. 55, pp. 374–375. 186 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 184 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... both to minimize roundoff...

Ngày tải lên: 24/12/2013, 12:16

... 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

... also p2, the 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 ... Integrals Integrals of functions of several variables, over regions with dimension greater than one, are not easy. There are two reasons for this. First, the number of function eva...

Ngày tải lên: 15/12/2013, 04:15

... Integrals Integrals of functions of several variables, over regions with dimension greater than one, are not easy. There are two reasons for this. First, the number of function evaluations needed ... power of the number needed to do a one-dimensional integral. If you need 30 function evaluations to do a one-dimensional integral crudely, then you will likely need on the order of 30...

Ngày tải lên: 15/12/2013, 04:15