BISECTION ALGORITHM
* To find a solution to f(x) = 0 given the continuous function
* f on the interval [a,b], where f(a) and f(b) have
* opposite signs:
*
* INPUT: endpoints a,b; tolerance TOL;
* maximum number of iterations N0.
*
* OUTPUT: approximate solution p or
* a message that the algorithm fails.
FIXED-POINT ALGORITHM
* To find a solution to p = g(p) given an
* initial approximation p0
*
* INPUT: initial approximation; tolerance TOL;
* maximum number of iterations NO.
*
* OUTPUT: approximate solution p or
* a message that the method fails.
HORNER'S ALGORITHM
* To evaluate the polynomial
* p(x) = a(n) * x^n + a(n-1) * x^(n-1) + ... + a(1) * x + a(0)
* and its derivative p'(x) at x = x0;
*
* INPUT: degree n; coefficients aa(0),aa(1),...,aa(n);
* value of x0.
*
* OUTPUT: y = p(x0), z = p'(x0).
METHOD OF FALSE POSITION
ALGORITHM
* To find a solution to f(x) = 0 given the continuous function
* f on the interval [p0,p1], where f(p0) and f(p1) have
* opposite signs:
*
* INPUT: endpoints p0, p1; tolerance TOL;
* maximum number of iterations N0.
*
* OUTPUT: approximate solution p or
* a message that the algorithm fails.
MULLER'S ALGORITHM
* To find a solution to f(x) = 0 given three approximations x0, x1
* and x2:
*
* INPUT: x0,x1,x2; tolerance TOL; maximum number of iterations NO.
*
* OUTPUT: approximate solution p or message of failure.
*
* This implementation allows for a switch to complex arithmetic.
* The coefficients are stored in the vector A, so the dimension
* of A may have to be changed.
NEWTON-RAPHSON ALGORITHM
* To find a solution to f(x) = 0 given an
* initial approximation p0:
*
* INPUT: initial approximation p0; tolerance TOL;
* maximum number of iterations NO.
*
* OUTPUT: approximate solution p or a message of failure.
SECANT ALGORITHM
* To find a solution to the equation f(x) = 0
* given initial approximations p0 and p1:
*
* INPUT: initial approximation p0, p1; tolerance TOL;
* maximum number of iterations N0.
*
* OUTPUT: approximate solution p or
* a message that the algorithm fails.
STEFFENSEN'S ALGORITHM
* To find a solution to g(x) = x
* given an initial approximation p0:
*
* INPUT: initial approximation p0; tolerance TOL;
* maximum number of iterations N0.
*
* OUTPUT: approximate solution p or
* a message that the method fails.