Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 3 pot

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 161 pot

... originally published, in different form, in Computers in Physics magazine, Copyrightc American Institute of Physics, 1988–1992.First Edition originally published 1988; Second Edition originally ... equations (Chapter 2), interpolation and extrapolation (Chaper 3), integration(Chaper 4), nonlinear root-ﬁnding (Chapter 9), eigensystems (Chapter 11), andordinary differential equations (Chapter ... Numerical Recipes is supposed to be “everything up to, butnot including, partial differential equations.” We honor this in the breach: First,we do have one introductory chapter on methods for partial...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 162 ppsx

... a single-screen license andpassword immediately, on-line, from the On-Line Store, with fees ranging from$50 (PC, Macintosh, educational institutions’ UNIX) to $140 (general UNIX).Downloading ... are available in IBM-compatible format for machinesrunning Windows 3.1, 95, or NT. CDROM versions in ISO-9660 format for PC,Macintosh,and UNIX systems are also available; these include both ... 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 (including this...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 163 potx

... method10.5 linmin minimum of a function along a ray in N-dimensions10.5 f1dim function used by linmin10.6 frprmn minimize in N-dimensions by conjugate gradient10.6 dlinmin minimum of a function ... qsimp integrate using Simpson’s rule4.3 qromb integrate using Romberg adaptive method4.4 midpnt extended midpoint rule4.4 qromo integrate using open Romberg adaptive method4.4 midinf integrate ... rotation used by qrupdt3.1 polint polynomial interpolation3.2 ratint rational function interpolation3.3 spline construct a cubic spline3.3 splint cubic spline interpolation3.4 locate search...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 164 pot

... linbcg more generalthat is dependent on First Edition routines, we do not recommend blindly replacingthem by the corresponding routines in this book. We do recommend that any newprogramming ... of Numerical Recipes in Pascaland Numerical Recipes Routines and Examples in BASIC are also available; whilenot containing the additional material of the Second Edition versions in C andFORTRAN, ... we include programs in the text, they look like this:#include <math.h>#define RAD (3.14159265/180.0)void flmoon(int n, int nph, long *jd, float *frac)Our programs begin with an introductory...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 165 potx

... dates to be searched.#define IYEND 2000int main(void) /* Program badluk */{void flmoon(int n, int nph, long *jd, float *frac);long julday(int mm, int id, int iyyy);int ic,icon,idwk,im,iyyy,n;float ... that task, giving incidentally all other Fridays the 13th as a by-product.#include <stdio.h>#include <math.h>#define ZON -5.0 Time zone −5 is Eastern Standard Time.#define IYBEG 1900 ... representations in most programming languages. You should learnto think about your programming tasks, insofar as possible, exclusively in terms ofthese standard control structures. In writing programs,...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 166 ppsx

... producing an integer result, throwing away any integer remainder. In floating-pointrepresentation, a number is represented internally by a sign bits (interpreted as plus or minus), an exact integer ... the function prototype of all Numerical Recipes routines that are called byother Numerical Recipes routines internally to the calling routine. (That also makesour routines much more readable.) ... zero-offsetthinking that C encourages but (as we see) does not require. A final liberating pointis that the utility file nrutil.c, listed in full in Appendix B, includes functionsfor allocating (using malloc())...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 167 pdf

... beevaluated by summing a ﬁnite number of leading terms in its in nite series, ratherthan all in nity terms. In cases like this, there is an adjustable parameter, e.g., thenumber of points or of terms, ... preferentially in one direction. In this case the total will be of order Nm.(ii) Some especially unfavorable occurrences can vastly increase the roundofferror of single operations. Generally ... 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 (including this...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 168 pot

... function at an intermediate point x and obtains a new, smallerbracketing interval, either (a, x) or (x, b). The process continues untilthe bracketinginterval is acceptably small. It is optimal ... the so-called “simplex algorithm”for linear programming problems.39410.1 Golden Section Search in One Dimension397Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... strongly on the particular interests of whomyou talk to. Economists, and some engineers, are particularly concerned withconstrained optimization, where there are apriorilimitations on the allowed valuesof...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 169 potx

... function at an intermediate point x and obtains a new, smallerbracketing interval, either (a, x) or (x, b). The process continues until the bracketinginterval is acceptably small. It is optimal ... than) the square root of your machine’s ﬂoating-point precision, sincesmaller values will gain you nothing.It remains to decide on a strategy for choosing the new point x,given(a, b, c).Suppose ... get a high third point.Our standard routine is this:#include <math.h>#include "nrutil.h"#define GOLD 1.618034#define GLIMIT 100.0#define TINY 1.0e-20#define SHFT(a,b,c,d)...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 170 docx

... your machine’s ﬂoating-point precision.#include <math.h>#include "nrutil.h"#define ITMAX 100#define CGOLD 0.3819660#define ZEPS 1.0e-10HereITMAX is the maximum allowed number ... points are collinear, in which case the denominator is zero (minimum of the parabola is in nitely far10.3 One-Dimensional Search with First Derivatives405Sample page from NUMERICAL RECIPES IN ... are 2 ×x ×tolapart, with x (the best abscissa) at the midpoint of a and b, and therefore fractionallyaccurate to ±tol.Indulge us a ﬁnal reminder that tol should generally be no smaller than thesquare...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 171 doc

... geometrical ﬁgure consisting, in N dimensions, of N +1points (or vertices) and all their interconnecting line segments, polygonal faces, etc. In two dimensions, a simplex is a triangle. In three dimensions ... 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 (including this ... 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 (including this...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 172 docx

... N +1 points, deﬁning an initial simplex. If you think of one of thesepoints (it matters not which) as being your initial starting point P0, then you cantake the other N points to bePi= ... minimizationroutine. Without bracketing, and with more than one independent variable, weno longer have the option of requiring a certain tolerance for a single independentvariable. We typically can ... routine name amoeba is intended to be descriptive of this kind ofbehavior; the basic moves are summarized in Figure 10.4.1.Termination criteria can be delicate in any multidimensional minimizationroutine....

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 173 ppsx

... along the line going through the point p in the direction xi. linmin calls ourfamiliar one-dimensional routines mnbrak (§10.1) and brent (§10.3) and instructsthem to minimize f1dim. linmin communicates ... have space to include such routines in thisbook. Our linmin,whichworks just fine, is instead a kind of bookkeeping swindle. It constructs an “artificial”function of one variable called f1dim, ... Successive minimizations along coordinate directions in a long, narrow “valley” (shownas contour lines). Unless the valley is optimally oriented, this method is extremely inefficient, takingmany tiny...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 174 docx

... DerivativesKindly reread the last part of §10.5. We here want to do the same thing, butusing derivative information in performing the line minimization.The modiﬁed version of linmin, called dlinmin, ... (which, incidentally, goes backto Cauchy), is similar to the problem that was shown in Figure 10.5.1. The methodwill perform many small steps ingoing down a long,narrow valley, even if the valleyis ... problem of minimizing a function approximated by the quadratic422Chapter 10. Minimization or Maximization of FunctionsSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 175 pps

... iterations.#define EPS 3.0e-8 Machine precision.#define TOLX (4*EPS) Convergence criterion on x values.#define STPMX 100.0 Scaled maximum step length allowed in line searches.#define FREEALL free_vector(xi,1,n);free_vector(pnew,1,n); ... corrected edition (Washington: Mathe-matical Association of America), pp. 467–468.10.8 Linear Programming and the SimplexMethodThe subject of linear programming, sometimes called linear optimization,concerns ... valid. All we are guaranteed is thatinitially f decreases as we move in the Newton direction. Once again we can usethe backtracking strategy described in §9.7 to choose a step along the direction...

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