opt_quadratic, an Octave code which interactively uses quadratic interpolation to estimate a critical point of a function f(x) given three starting points, an iteration limit n, and tolerances for x and y.
The user enters a formula for f(x), the starting values x1, x2, x3, the iteration limit n, and tolerances for the size of the final x and y intervals.
The program returns an estimate for a critical point x, which might be a minimum, maximum or just an inflection point. It also returns the number of iterations.The program can be invoked by a function call, in which case the string specifying f(x) must be quoted:
[ x, it ] = opt_quadratic ( 'x^2+sin(4*x)', -1, 1, 2, 25, 0.00001, 0.000001 )
or, if called with no arguments, it will request them:
[ x, it ] = opt_quadratic ( );
Enter function formula, like x^2: x^2+sin(4*x)
Enter point 1, x1: -1
Enter point 2, x2: 1
Enter point 3, x3: 2
Enter number of iterations, n: 25
Enter x tolerance: 0.00001
Enter y tolerance: 0.00001
The function is specified as a string which is either:
The string should not contain any spaces between symbols, except when it is passed as a function argument in quotes.
It is not necessary to use the "dot" notation for expressions involving '*', '/', or '^', but it doesn't hurt either.
Examples of function specifications:
x^2
x.^2
3/(x^4+5*x-6)
sin(7*x)*sqrt(x)/8
wiggle(x) <-- where "wiggle.m" is a user-provided M file.
The information on this web page is distributed under the MIT license.
opt_quadratic is available in a MATLAB version and an Octave version.
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