[section:minimax Minimax Approximations and the Remez Algorithm]
-The directory libs/math/minimax contains a command line driven
+The directory `libs/math/minimax` contains an interactive command-line driven
program for the generation of minimax approximations using the Remez
algorithm. Both polynomial and rational approximations are supported,
although the latter are tricky to converge: it is not uncommon for
To use this tool, you will need to have a reasonable grasp of what the Remez
algorithm is, and the general form of the approximation you want to achieve.
-Unless you already familar with the Remez method,
-you should first read the [link math_toolkit.remez
-brief background article explaining the principles behind the
-Remez algorithm].
+Unless you already familar with the Remez method, you should first read the
+[link math_toolkit.remez brief background article explaining the principles behind the Remez algorithm].
The program consists of two parts:
approximation: for example if you are approximating a function
/f(x)/ then it is quite common to use:
- f(x) = g(x)(Y + R(x))
+[expression f(x) = g(x)(Y + R(x))]
where /g(x)/ is the dominant part of /f(x)/, /Y/ is some constant, and
/R(x)/ is the rational approximation part, usually optimised for a low
absolute error compared to |Y|.
-In this case you would define /f/ to return ['f(x)/g(x)] and then set the
+In this case you would define /f/ to return [role serif-italic f(x)/g(x)] and then set the
y-offset of the approximation to /Y/ (see command line options below).
Many other forms are possible, but in all cases the objective is to
x and y offsets, and of course the coefficients of the polynomials.]]
]
-
-[endsect][/section:minimax Minimax Approximations and the Remez Algorithm]
+[endsect] [/section:minimax Minimax Approximations and the Remez Algorithm]
[/
Copyright 2006 John Maddock and Paul A. Bristow.