Tài liệu Evaluation of Functions part 5 doc

... nPn−1(x) (5. 5.1)Jn+1(x)=2nxJn(x)−Jn−1(x) (5. 5.2)nEn+1(x)=e−x−xEn(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)176Chapter 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 ... methods from two successive values of n toother values, either larger or smaller.Equations (5. 5.4)and (5. 5 .5) motivate us to say a few words about trigonometric functions. If your program’s running...

Tài liệu Integration of Functions part 5 docx

... rest of the routine is exactly likemidpntand is omitted.142Chapter 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 OrthogonalPolynomialsIn the formulas of §4.1, the integral of a function was approximated by the sum of its functional values at a set of equally ... extrapolation, afterjust 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...

Tài liệu Evaluation of Functions part 1 docx

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Tài liệu Evaluation of Functions part 2 doc

... America).Chapter 5. Evaluation of Functions 5. 0 IntroductionThe purpose of this chapter is to acquaint you with a selection of the techniquesthat are frequently used in evaluating functions. In ... Similarly, the form of the coefﬁcients a is often such as to makeuse of previous work: Terms like k! or (2k)! can be updated in a multiply or two.1 65 168Chapter 5. Evaluation of Functions Sample ... 166Chapter 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...

Tài liệu Evaluation of Functions part 12 doc

... ≡Mk=0akxk1+Nk=1bkxk (5. 12.1)198Chapter 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 ... 200Chapter 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 ... Mathe-matical Association of America), pp. 59 , 182–183 [synthetic division]. 5. 11 Economization of Power SeriesOne particular application of Chebyshev methods, the economization of power series,isan...

Tài liệu Evaluation of Functions part 5 ppt

... ···+qkxki)i=1,2, ,m+k+1 (5. 13.4)202Chapter 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]xN)/(1 +cof[n+1]x + ···+ 5. 12 Pad´e Approximants203Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright ... vol. 7 65, L. Wuytack, ed. (Berlin: Springer-Verlag). [1]200Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright...

Tài liệu Evaluation of Functions part 8 doc

... inpolynomial approximation of functions. 186Chapter 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 ... equations (5. 7.4). This forces temp into andout of addressable memory.188Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright ... 190Chapter 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...

Tài liệu Evaluation of Functions part 9 docx

... 192Chapter 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;190Chapter 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 ... inpolynomial approximation of functions. 5. 8 Chebyshev Approximation191Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0 -52 1-43108 -5) Copyright (C) 1988-1992...

Tài liệu Modeling of Data part 5 doc

... ×∇χ2(acur)( 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 χ2function at any set of parameters ... Use of the Normal EquationsThe minimum of ( 15. 4.3) occurs where the derivative of χ2with respect to allM parameters akvanishes. Specializing equation ( 15. 1.7) to the case of the model( 15. 4.2), ... svdcmp.Equation ( 15. 4.17) says that the ﬁtted parameters a are linear combinations of the columns of V, with coefﬁcients obtained by forming dot products of the columns672Chapter 15. Modeling of DataSample...

Tài liệu Integration of Functions part 3 docx

... twice themagnitude of the ﬁrst neglected term. The reason that it is not convergent is thatthe Bernoulli numbers become very large, e.g.,B 50 =4 950 572 052 4107964821247 752 566The key point ... Cliffs, NJ: Prentice-Hall),§ 5. 3.138Chapter 4. Integration 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 ... 136Chapter 4. Integration 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 University...

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