Tài liệu Evaluation of Functions part 5 ppt

... 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 0 -52 1-43108 -5) Copyright ... original coefficient values. 202 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyrig...

Ngày tải lên: 24/12/2013, 12:16

... this: f(x)=b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 + a 5 b 5 +··· (5. 2.1) Printers prefer to write this as f(x)=b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 + a 5 b 5 + ··· (5. 2.2) In either (5. 2.1) or (5. 2.2), the a’s and b’s can themselves be functions ... 1970, Mathematical Methods of Physics , 2nd ed. (Reading, MA: W.A. Benjamin/Addison-Wesley), § 2.3. [2] 5. 2 Evalu...

Ngày tải lên: 15/12/2013, 04:15

... {dp=dp*x+p; p=p*x+c[j];} 174 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright (C) 1988-1992 by Cambridge ... =a 0 −B 4 −B 2 (C+D)−CD (5. 3.3) 5. 3 Polynomials and Rational Functions 1 75 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5)...

Ngày tải lên: 15/12/2013, 04:15

... 176 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright (C) 1988-1992 by Cambridge ... 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 + .....

Ngày tải lên: 24/12/2013, 12:16

... suitable for evaluation by the routine ratval in 5. 3. 206 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright ... 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=dv...

Ngày tải lên: 24/12/2013, 12:16

... − (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 -52 1-43108 -5) Copyright (C) 1988-1992 ... implementation of this algorithm is given in §6.12 as the routine hypgeo. 210 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF S...

Ngày tải lên: 24/12/2013, 12:16

... nP n−1 (x) (5. 5.1) J n+1 (x)= 2n x J n (x)−J n−1 (x) (5. 5.2) nE n+1 (x)=e −x −xE n (x) (5. 5.3) cos nθ =2cosθcos(n − 1)θ − cos(n − 2)θ (5. 5.4) sin nθ =2cosθsin(n − 1)θ − sin(n − 2)θ (5. 5 .5) where ... are f(x)=β(1,x)F 0 (x)y 2 +F 1 (x)y 1 +F 0 (x)c 0 (5. 5.23) Equations (5. 5.21) and (5. 5.23) are Clenshaw’srecurrence formula for doing the sum (5. 5.19): You make one pass down through...

Ngày tải lên: 24/12/2013, 12:16

... y −1 =0 (5. 5. 25) y k = 1 β(k +1,x) [y k−2 −α(k, x)y k−1 − c k ], (k =0,1, ,N−1) (5. 5.26) f(x)=c N F N (x)−β(N, x)F N−1 (x)y N−1 − F N (x)y N−2 (5. 5.27) The rare case where equations (5. 5. 25) – (5. 5.27) ... (5. 5. 25) – (5. 5.27) should be used instead of equations (5. 5.21) and (5. 5.23) can be detected automatically by testing whether the operands in the first sum in (5. 5.23) are...

Ngày tải lên: 24/12/2013, 12:16

... { cint[j]=con*(c[j-1]-c[j+1])/j; Equation (5. 9.1). 196 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright (C) 1988-1992 ... 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 o...

Ngày tải lên: 24/12/2013, 12:16

... extrapolation, after just 5 calls to trapzd, while qsimp requires 8 calls (8 times as many evaluations of the integrand) and qtrap requires 13 calls (making 256 times as many evaluations of the integrand). CITED ... rest of the routine is exactly like midpnt and is omitted. 146 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