nonlin_newton


nonlin_newton, a MATLAB code which interactively applies Newton's method to seek a root of a function given formulas for f(x), f'(x), and a starting value a.

The user enters formulas for f(x), f'(x), and the value a.

The program then repeatedly applies Newton's method until it encounters a very small function value or it detects a problem with the iteration.

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

        [ a, fa, it ] = nonlin_newton ( 'cos(x)-x', '-sin(x)-1', 0 )
      
or as an interactive command with arguments:
        [ a, fa, it ] = nonlin_newton cos(x)-x -sin(x)-1 0
      
or, if called with no arguments, it will request them:
        [ a, fa, it ] = nonlin_newton ( );
        Enter function formula, like x^2: cos(x)-x
        Enter derivative formula, like 2*x: -sin(x)-1
        Enter starting point, a: 0
      

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.
      

Licensing:

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

Languages:

nonlin_newton is available in a MATLAB version.

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Source Code:


Last revised on 07 July 2019.