|PGnumericalmacros.pl||topic started 5/22/2000; 9:56:06 PM
last post 5/22/2000; 9:56:06 PM
|Michael Gage - PGnumericalmacros.pl
5/22/2000; 9:56:06 PM (reads: 950, responses: 0)
Numerical methods for the PG language
Usege: $fn = horner([x0,x1,x2],[q0,q1,q2]);
Generates a subroutine which evaluates a polynomial passing through the points
Usage: $poly = hermit([x0,x1...],[y0,y1...],[yp0,yp1,...]);
Generates a subroutine which evaluates a polynomial passing through the specified points with the specified derivatives: (x0,y0,yp0) ... The polynomial will be of high degree and may wobble unexpectedly. Use the Hermite splines described below and in Hermite.pm for most graphing purposes.
Usage: $spline = hermit_spline([x0,x1...],[y0,y1...],[yp0,yp1,...]);
&$spline(45) evaluates to a number.
Generates a subroutine which evaluates a piecewise cubic polynomial passing through the specified points with the specified derivatives: (x0,y0,yp0) ...
An object oriented version of this is defined in Hermite.pm
Where the x and y value arrays come from the function to be approximated. The function reference will take a single value x and produce value y.
$y = &$fun_ref($x);
The string contains
and can be placed in the header of the HTML output using
Usage: trapezoid(function_reference, start, end, steps=>30 );
Implements the trapezoid rule using 30 intervals between 'start' and 'end'. The first three arguments are required. The final argument (number of steps) is optional and defaults to 30.
Usage: romberg(function_reference, x0, x1, level);
Implements the Romberg integration routine through 'level' recursive steps. Level defaults to 6.
Usage: inv_romberg(function_reference, a, value);
Finds b such that the integral of the function from a to b is equal to value. Assumes that the function is continuous and doesn't take on the zero value. Uses Newton's method of approximating roots of equations, and Romberg to evaluate definite integrals.
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