HELP FOR PROGRAM NLINSYST
This program solves a nonlinear system of two variables:
f(x,y) = 0
g(x,y) = 0
We use here a generalized Newton's method called linearization
method.
Starting from an initial point, (x0,y0), two series, Xn and Yn,
are built, converging towards the system solution, alpha, beta.
The series are defined by:
fg'y - gf'y
Xk+1 = Xk - -------------
delta
gf'x - fg'x
Yk+1 = Yk - -------------
delta
with delta = f'x.g'y - f'y.g'x
f'x = partial derivative of f with respect to x
f'y = partial derivative of f with respect to y
g'x = partial derivative of g with respect to x
g'y = partial derivative of f with respect to y
The program stops when quantity |Xn-Xn+1| + |Yn-Yn+1| < required precision.
Final Xn, Yn give an approximate system solution.
REFERENCE: "Mathematiques en Turbo-Pascal part 1, By M. Ducamp and
A. Reverchon, Editions EYROLLES, Paris, 1987".