Tài liệu Evaluation of Functions part 14 ppt

... 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); 5.13 ... **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; Numbe...

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 ... necessarily including the domain of convergence of the series, however). Sometimes the continued fraction converges best where the series does worst, although this is...

Ngày tải lên: 15/12/2013, 04:15

... generalizes to 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 of a polynomial of degree nc as ... 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: THE ART...

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 ... approximation in the interval of interest, by the methods of §5.8. We would have obtained just the same lower-order polynomial. The principal lesson is that the rate of convergence of...

Ngày tải lên: 24/12/2013, 12:16

... − z)F  = abF − [c − (a + b +1)z]F  (5 .14. 2) 5 .14 Evaluation of Functions by Path Integration 209 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... Digital Computers (New York: Wiley), Chapter 13. [1] 5 .14 Evaluation of Functions by Path Integration In computer programming, the technique of choice is not necessa...

Ngày tải lên: 24/12/2013, 12:16

... 178 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... relation is of little or no practical use in that direction. This is the case, e.g., for (5.5.2) in the direction of increasing n,whenx<n. You cannot generate Bessel functions of high n by ... Introduction) [1] give a list o...

Ngày tải lên: 24/12/2013, 12:16

... 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 algebra. Yet, surprisingly ... b, c, namely x = −b ± √ b 2 − 4ac 2a (5.6.2) 184 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-4...

Ngày tải lên: 24/12/2013, 12:16

... quadrature [1] . It is often combined with an adaptive choice of N, the number of Chebyshev coefficients calculated via equation (5.8.7), which is also the number of function evaluations of f(x). If a ... 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 ....

Ngày tải lên: 24/12/2013, 12:16

... numerical stability is greatly improved if, instead of using powers of x as a set of basis functions to represent the p j ’s, one uses some other known set of orthogonal polynomials π j (x), say. Roughly ... 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 f...

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