**approx_chebyshev**,
a MATLAB code which
interactively approximates a function f(x) in the interval [a,b]
by constructing a Chebyshev polynomial interpolant that is often
a good estimate of the minmax polynomial.

The user enters a formula for f(x), and the values of a and b, and the number of Chebyshev interpolation points n.

The program computes the corresponding n-1 degree interpolating polynomial, estimates the maximum approximation error over [a,b], and returns the interpolant value at 101 points in [a,b].

The program can be invoked by a function call, in which case the string specifying f(x) must be quoted:

[ xp, yp, maxerr ] = approx_chebyshev ( 'x^2', -1, 3, 11 );or, if called with no arguments, it will request them:

[ xp, yp, maxerr ] = approx_chebyshev ( ); Enter function formula, like x^2: x^2 Enter left limit, a: -1 Enter right limit, b: 3 Enter number of interpolation points: 11

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.

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

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- approx_chebyshev.m the source code.