**approx_leastsquares**,
a MATLAB code which
interactively approximates a function f(x) in the interval [a,b]
by constructing an m-degree polynomial which minimizes the square
root of the sum of the squares of the error with n sample data points.

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

The program computes the corresponding m degree polynomial, computes the root-mean-square (RMS) norm of the difference between the approximant polynomial and the data values, and returns the approximant polynomial 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, rmserr ] = approx_leastsquares ( 'sin(x)', -1, 3, 9, 51 );or, if called with no arguments, it will request them:

[ xp, yp, rmserr ] = approx_leastsquares ( ); Enter function formula, like x^2: sin(x) Enter left limit, a: -1 Enter right limit, b: 3 Enter degree of approximation polynomial: 9 Enter number of interpolation points: 51

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_leastsquares** is available in
a MATLAB version.

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- approx_leastsquares.m the source code.