BROYDEN ALGORITHM
*
* To approximate the solution of the nonlinear system F(X) = 0
* given an initial approximation X.
*
* INPUT: Number n of equations and unknowns; initial
* approximation X = (X(1),...,X(n)); tolerance TOL;
* maximum number of iterations N.
*
* OUTPUT: Approximate solution X = (X(1),...,X(n)) or a message
* that the number of iterations was exceeded.
CONTINUATION
METHOD FOR SYSTEMS ALGORITHM
*
* To approximate the solution of the nonlinear system F(X)=0 given
* an initial approximation X:
*
* INPUT: Number n of equations and unknowns; initial approximation
* X=(X(1),...,X(n)); Number of Runge-Kutta 4 iterations N1
*
* OUTPUT: Approximate solution X=(X(1),...,X(n))
NEWTON'S
METHOD FOR SYSTEMS ALGORITHM
*
* To approximate the solution of the nonlinear system F(X)=0 given
* an initial approximation X:
*
* INPUT: Number n of equations and unknowns; initial approximation
* X=(X(1),...,X(n)); tolerance TOL; maximum number of
* iterations N.
*
* OUTPUT: Approximate solution X=(X(1),...,X(n)) or a message
* that the number of iterations was exceeded.
STEEPEST DESCENT ALGORITHM
*
* To approximate a solution P to the minimization problem
* G(P) = MIN( G(X) : X in R(n) )
* given an initial approximation X:
*
* INPUT: Number n of variables; initial approximation X;
* tolerance TOL; maximum number of iterations N.
*
* OUTPUT: Approximate solution X or a message of failure.