 |
 |
 |
||||||||
 |
||||||||||
 |
||||||||||
 |
Newton's Method for n Non-Linear equations In Newton's method for 1 dimension, a function g is needed such that g(x) = x where x is the root of f. Such a function g maybe written as g(x) = x - q(x)f(x)……where q(x) = 1/f'(x) Similarly for a system of n nonlinear equations in the unknowns x1, x2, … xn described by F = (x1,x2, ... xn), where F is a vector valued function, can be solved using a matrix G(x) = x - invA(x)F(x) where A is matrix akin to q as in the 1-dimensional. Click here to view the proof, examples and MATLAB coding.
Next ... Part 2: Solving ODEs |
|||||||||
 |
||||||||||
 |
||||||||||
 |
||||||||||
 |
||||||||||
 |
||||||||||
 |
||||||||||
 |
 |
|||||||||
