Site Statistics  |   Contact  |   About Us Tuesday, December 11, 2018
HOME › AREAS OF EXPERTISE › Nonlinear Systems Applications › ~ Fixed Point / Birge-Vieta Methods

FIXED POINT METHOD
Fixed Point

The idea behind the fixed point method is very simple: to find the solutions of a given nonlinear function f(x) = 0, it is possible to rearrange f(x)= 0 into the form x = g(x), where g(x) denotes a function of x. Then, simply start with an initial guess, x0 and apply the iteration process:

 xn = g(xn - 1)     for n = 1,2,3,...

For example, to find solutions for the following nonlinear equation:

 f(x) = sin x + ex + x2 - 2x = 0

There are several ways to rewrite the above equation into the form x = g(x). For example, it is possible to rearrange the above equation into the following form:

 x = 1/2(sin x + ex + x2)

Or can be rearranged as:

 x = √2x - sin x - ex

 You are viewing this tab ↓

Math, Analysis & More,
established expertise..."

EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method

INTERPOLATION APPLICATIONS...
Cubic Spline Method
Newton Divided Difference

 Applied Mathematical Algorithms
 Complex Functions A complex number z = x + iy, where... Complex Functions Non-Linear Systems Non-linear system methods... Non Linear Systems Differentiation Construction of differentiation... Differentiation Integration Consider the function where... Integration