**opt_golden**,
a MATLAB code which
interactively estimates a minimizer of a function f(x)
over the interval [a,b], assuming f(x) is unimodular ("U-shaped") over [a,b].

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_golden ( '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_golden ( ); 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:

- a MATLAB expression using the argument 'x';
- the name of an M-file followed by the argument '(x)'.

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 computer code and data files made available on this web page are distributed under the GNU LGPL license.

**opt_golden** is available in
a MATLAB version.

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opt_quadratic, a MATLAB 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.

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quad_gauss, a MATLAB code which interactively uses an n-point Gauss quadrature rule to estimate the integral of a function f(x) in the interval [a,b].

quad_monte_carlo, a MATLAB code which interactively uses n random samples to estimate the integral of a function f(x) in the interval [a,b].

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- opt_golden.m the source code.