Tài liệu Evaluation of Functions part 1 docx

Ngày tải lên: 15/12/2013, 04:15

... terms of the T n ’s — see equations 5 .11 .2-5 .11 .3.) The Chebyshev polynomials are orthogonalin the interval [ 1, 1] over a weight (1 − x 2 ) 1/ 2 . In particular,  1 1 T i (x)T j (x) √ 1 − x 2 dx ... Figure 5.8 .1) , T 0 (x) =1 T 1 (x)=x T 2 (x)=2x 2 1 T 3 (x)=4x 3 −3x T 4 (x)=8x 4 −8x 2 +1 ··· T n +1 (x)=2xT n (x)− T n 1 (x) n ≥ 1. (5.8.2) (There also exist inverse...

Ngày tải lên: 24/12/2013, 12:16

... formulas of higher order for this situation, but we will refrain from giving them. The semi-open formulas arejusttheobviouscombinations ofequations(4 .1. 11) – (4 .1. 14) with (4 .1. 15)–(4 .1. 18), respectively. ... function t e t − 1 = ∞  n=0 B n t n n! (4.2.2) with the first few even values (odd values vanish except for B 1 = 1/ 2) B 0 =1 B 2 = 1 6 B 4 =− 1 30 B 6 = 1 42 B 8...

Ngày tải lên: 15/12/2013, 04:15

... 14 0 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge University ... Copyright (C) 19 88 -19 92 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of...

Ngày tải lên: 15/12/2013, 04:15

... with (4 .1. 11) the “deep” property 14 2 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by ... Integrals 14 1 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge University Press.Pro...

Ngày tải lên: 15/12/2013, 04:15

... multiply or two. 16 5 16 6 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge University ... estimate. } else { tmp=wksp [1] ; wksp [1] =term; for (j =1; j<=nterm -1; j++) { Update saved quantities by van Wijn- gaarden’s algorithm.dum=wksp[j +1] ; 16 8 Chapt...

Ngày tải lên: 15/12/2013, 04:15

... 5 .10 Polynomial Approximation from Chebyshev Coefficients 19 7 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge ... coefficient array c[0 n -1] , this routine generates a coefficient array d[0 n -1] such that  n -1 k=0 d k y k =  n -1 k=0 c k T k (y) − c 0 /2.Themethod is Clenshaw’s recurrence (5.8...

Ngày tải lên: 15/12/2013, 04:15

... 19 8 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge University ... Work ; 19 90, corrected edition (Washington: Mathe- matical Association of America), pp. 59, 18 2 18 3 [synthetic division]. 5 .11 Economization of Power Series One particular applicatio...

Ngày tải lên: 15/12/2013, 04:15

... part of (5.2.2) is f even = d 0 + c 1 d 1 + c 2 d 2 + ··· (5.2 .12 ) where in terms of intermediate variables α 1 = a 1 b 1 α n = a n b n b n 1 ,n≥2 (5.2 .13 ) we have d 0 = b 0 ,c 1 =α 1 ,d 1 =1+ α 2 c n =−α 2n 1 α 2n−2 ,d n =1+ α 2n 1 +α 2n ,n≥2 (5.2 .14 ) You ... b 0 ,c 1 =α 1 ,d 1 =1+ α 2 c n =−α 2n 1 α 2n−2 ,d n =1+ α 2n 1 +α 2n ,n≥2 (5.2 .14 ) You can...

Ngày tải lên: 15/12/2013, 04:15

... simultaneously: p=c[n]; dp=0.0; for(j=n -1; j>=0;j ) {dp=dp*x+p; p=p*x+c[j];} 17 4 Chapter 5. Evaluation of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 ... Rational Functions 17 3 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyrigh...

Ngày tải lên: 15/12/2013, 04:15