NUMERICAL METHODS FOR COMPUTING OLS ESTIMATES

| is sufficiently small. This is usually the case,but by no means guaranteed. Jones[7]gives a list of theorems that can be used tojustify this termination criterion for various kinds of continued fractions.There is atpresent no rigorousanalysis oferrorpropagationinLentz’s algorithm.However, em[r]

“adaptive” choices of stepsize. We will not, therefore, develop that material here.If the function that you propose to integrate is sharply concentrated in one or morepeaks, or if its shape is not readily characterized by a single length-scale, then itis likely that you should cast the problem in th[r]

5.2 Evaluation of Continued Fractions169Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted fo[r]

We usually also need to know the accuracy with which parameters are de-termined by the data set. In other words, we need to know the likely errors ofthe best-fit parameters.Finally, it is not uncommon in fitting data to discover that the merit functionis not unimodal, with a single minimum. In some ca[r]

1.1 Program Organization and Control Structures5Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is grant[r]

or else they will grow old and die, and then your hypothesis will become accepted.Sounds crazy, we know, but that’s how science works!In this book we make a somewhat arbitrary distinction between data analysisprocedures that are model-independent and those that are model-dependent.Intheformer catego[r]

1.1 Program Organization and Control Structures5Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is grant[r]

optimizing hard numerical functions based on simulating the social behavior of bees and how can reach the location ofmost flower concentration. In [13], a discrete particle swarm optimization (DPSO) algorithm was used as new algorithmfor solving the reconfiguration problems.The DPSO algorithm[r]

Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper c[r]

Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 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 machine-readable files (incl[r]

Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper c[r]

≤ 10−5. 4.2Our numerical experiments show that for 10−1≤ μ ≤ 10−6and 32 ≤ N ≤ 1024, oneach time level the number of iterations for monotone method 3.7 on the piecewise uniformmesh is independent of μ and N and equal 4, 4, and 3 for τ  0.1, 0.05, 0.01, respectively.Th[r]

differential-difference equations: mixed type of shifts wtih layer behavior,” International Journal ofComputer Mathematics, vol. 81, no. 1, pp. 49–62, 2004.15 H. Tian, Numerical treatment of singularly perturbed delay differential equations, Ph.D. thesis, Departmentof Mathematics, University o[r]

2.5 Iterative Improvement of a Solution to Linear Equations55Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permis[r]

material from an earlier section.The topics selected for inclusion are fairly standard, but not encyclopedic. Emergingareas of numerical analysis, such as wavelets, are not (in the author's opinion) appropriatefor a first course in the subject. The same reasoning dictated the exclusion[r]

configurable computing architectures, in algorithm imple-mentation methods, and in automatic mapping methods ofalgorithms onto hardware and processor spaces, indicatingthe changes in codesign flow due to the introduction of new,reconfigurable hardware platform. Using this platform,[r]

d.{int k,j;float fac,cnst;cnst=2.0/(b-a);fac=cnst;for (j=1;j<n;j++) { First we rescale by the factor const d[j] *= fac;fac *= cnst;}cnst=0.5*(a+b); which is then redefined as the desired shift.for (j=0;j<=n-2;j++) We accomplish the shift by synthetic division. Syntheticdiv[r]

configurable computing architectures, in algorithm imple-mentation methods, and in automatic mapping methods ofalgorithms onto hardware and processor spaces, indicatingthe changes in codesign flow due to the introduction of new,reconfigurable hardware platform. Using this platform,[r]

= z0+ hf(x, z0)zm+1= zm−1+2hf(x + mh, zm) for m =1,2, ,n−1y(x+H)≈yn≡12[zn+zn−1+hf(x + H, zn)](16.3.2)16.3 Modified Midpoint Method723Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.[r]

0,y(x0)=z0(16.5.1)As usual, y can denote a vector of values.Stoermer’s rule, dating back to 1907, has been a popular method for discretizing suchsystems. With h = H/m we havey1= y0+ h[z0+12hf(x0,y0)]yk+1− 2yk+ y