nonlin_fixed_point, a MATLAB code which interactively uses fixed point iteration x=g(x) to seek a zero of a function f(x) given a starting point x0 and a number of iterations it;
The user enters formulas for f(x), g'(x), the starting value x0, and the number of iterations.
The program carries out it iterations of the fixed point method, returning vectors of the n+1 elements of the sequence of x and f(x) values.
The program can be invoked by a function call, in which case the strings specifying f(x) and g(x) must be quoted:
[ x, fx, it ] = nonlin_fixed_point ( 'x^2-5', '(x+5/x)/2', 1.0, 10 )
or, if called with no arguments, it will request them:
[ x, fx, it ] = nonlin_fixed_point ( );
Enter function formula, like x^2: x^2-5
Enter fixed point formula, like 2*x: (x+5/x)/2
Enter starting point, x0: 1.0
Enter number of iterations, it: 10
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 computer code and data files made available on this web page are distributed under the MIT license
nonlin_fixed_point is available in a MATLAB version.
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