Tài liệu Modeling of Data part 3 docx

... [1] 15.2 Fitting Data to a Straight Line A concrete example will make the considerations of the previous section more meaningful. We consider the problem of fitting a set of N data points (x i ,y i )to a ... model y(x)=y(x;a, b)=a+bx (15.2.1) 662 Chapter 15. Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyri...

Ngày tải lên: 15/12/2013, 04:15

... 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Chapter 15. Modeling of Data 15.0 Introduction Given a set of observations, one often wants to ... underlying theory that the data are supposed to satisfy; examples are coefficients of rate equations in a complex network of chemical reactions, or orbital elements of a binary sta...

Ngày tải lên: 15/12/2013, 04:15

... statistical universe of data sets that are drawn from it! 658 Chapter 15. Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright ... are often taught, rather casually, that, on average, measurements will fall within ±σ of the true value 68 percent of the time, within ±2σ 95 percent of the time, and within 3...

Ngày tải lên: 15/12/2013, 04:15

... variance of the linear combination y i − a − bx i of two random variables x i and y i , Var(y i − a − bx i )=Var(y i )+b 2 Var(x i )=σ 2 yi +b 2 σ 2 xi ≡1/w i (15 .3. 3) The sum of the square of N ... value of s is known from having found the point B. The value of r follows from equations (15 .3. 2) and (15 .3. 3) applied at the χ 2 minimum (point O in the figure), giving r 2 =1 ...

Ngày tải lên: 15/12/2013, 04:15

... factor of 3 on the linear algebra by switching to LU decomposition, without 674 Chapter 15. Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright ... matrix. Solution by 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. Spe...

Ngày tải lên: 15/12/2013, 04:15

... therefore have the dimensions of a 2 k . Scan 684 Chapter 15. Modeling of Data Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) 1988-1992 ... method, attempting to reduce the value χ 2 of a fit between a set of data points x[1 ndata] , y[1 ndata] with individual standard deviations sig[1 ndata] , and a nonlinear funct...

Ngày tải lên: 15/12/2013, 04:15

... ellipses themselves — contain 68 .3% , 90%, and 99% of normally distributed data. The ellipse that contains 68 .3% of normally distributed data is shown dashed, and has ∆χ 2 =2 .30 . For additional numerical ... 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). actual data set  hypothetical data set hypothetical data set hypo...

Ngày tải lên: 15/12/2013, 04:15

... *arr,d,sum=0.0; arr=vector(1,ndatat); for (j=1;j<=ndatat;j++) arr[j]=yt[j]-b*xt[j]; if (ndatat & 1) { aa=select((ndatat+1)>>1,ndatat,arr); } else { j=ndatat >> 1; aa=0.5*(select(j,ndatat,arr)+select(j+1,ndatat,arr)); } abdevt=0.0; for ... Notice that the evaluation of the right-hand side of (15.7.16) occurs in the function rofunc, with communication via global (top-leve...

Ngày tải lên: 15/12/2013, 04:15

... term decreasing as 1/N 3 whichisclosedontherightandopenontheleft:  x N x 1 f(x)dx = h  23 12 f 2 + 7 12 f 3 + f 4 + f 5 + ···+f N−2 + 13 12 f N −1 + 5 12 f N  + O  1 N 3  (4.1.20) CITED REFERENCES ... the combination S = 4 3 S 2N − 1 3 S N (4.2.4) will cancel out the leading order error term. But there is no error term of order 1/N 3 , by (4.2.1). The surviving error is...

Ngày tải lên: 15/12/2013, 04:15

... calcium compounds to cause arteriosclerosis, hardening of the arteries. Arteriosclerosis means (“hardening of the arteries”) 2. The upper part of the heart on the left side, the left atrium, receives ... figure of Mickey alongside its statues of other eminent film stars. In 1 933 , according to Disney Studios, Mickey received 800,000 fan letters—an average of more than 2,000 let...

Ngày tải lên: 14/12/2013, 13:15