Tài liệu Evaluation of Functions part 5 doc

... 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 ... δ)=sinθ−[αsin θ − β cos θ] (5. 5.6) 176 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyri...

Ngày tải lên: 24/12/2013, 12:16

... rest of the routine is exactly like midpnt and is omitted. 142 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright ... Springer-Verlag), § 3.7, p. 152 . 4 .5 Gaussian Quadratures and Orthogonal Polynomials In the formulas of §4.1, the integral of a function was approximated by the sum of...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 15/12/2013, 04:15

... ≡ M  k=0 a k x k 1+ N  k=1 b k x k (5. 12.1) 198 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 ... 200 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...

Ngày tải lên: 15/12/2013, 04:15

... ···+q k x k i ) i=1,2, ,m+k+1 (5. 13.4) 202 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 ... 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...

Ngày tải lên: 24/12/2013, 12:16

... 192 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 ... k,j; float fac,bpa,bma,*f; 190 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 Cambridg...

Ngày tải lên: 24/12/2013, 12:16

... ×∇χ 2 (a cur )( 15. 5.3) where the constant is small enough not to exhaust the downhill direction. To use ( 15. 5.2) or ( 15. 5.3), we must be able to compute the gradient of the χ 2 function at any set of parameters ... Use of the Normal Equations The minimum of ( 15. 4.3) occurs where the derivative of χ 2 with respect to all M parameters a k vanishes. Specializing equation ( 15....

Ngày tải lên: 15/12/2013, 04:15

... twice the magnitude of the first neglected term. The reason that it is not convergent is that the Bernoulli numbers become very large, e.g., B 50 = 4 950 572 052 4107964821247 752 5 66 The key point ... Cliffs, NJ: Prentice-Hall), § 5. 3. 138 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyrigh...

Ngày tải lên: 15/12/2013, 04:15