Newton's method (applet) Paul Garrett, garrett@math.umn.edu

Newton's method (or the Newton-Raphson method) is a simple iterative numerical method to approximate roots of equations: Given one approximation, the idea is to go up to the graph, and then slide down the tangent to the x-axis to obtain the next approximation. In symbols, the sequence of approximate roots x0, x1, x2, x3, ... is created by the rule

xn+1 = xn - f(xn)/f'(xn)
where f is the function whose roots we want, and f' is its derivative.

-> Try various initial points to compare how quickly a true root is approached.
-> Note that it is harder to approach "middle" roots than the largest and smallest.
-> See Pathological Example to see what can go wrong.

© 1997, Paul Garrett ... [ garrett@math.umn.edu ]
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