CSC270 Tutorial on Root Finding

A ``root'' or ``zero'' of a function f(x) is a value z at which f(z) = 0. Root finding is used in many applications.

See the lecture notes on the Newton and Secant methods of root finding. The bisection method, which is not described in the notes, just keeps dividing a root-containing interval in half. This interval [a,b] must be initially chosen such that f(a)*f(b) < 0 (i.e. there must be a root in [a,b]).

Instructions

Select a root finding method and a function with the buttons on the graph.
Click on the graph to select an initial point or two, depending upon the root finding method.
Keep clicking to see the root finding in action.
The point turns green when the root is found. Click to restart.
The scrollbar changes magnification.
Drag the mouse while holding down a button to shift the axes.

Things to check out

What happens when bisection starts with the same sign of function on each end of the interval? Try several functions.
What happens when the various methods are searching for a double root, like with the x^2 function?
How does convergence compare with the various methods?
Is $|f(x)| < epsilon$ a good test for the termination of the Newton and secant methods? Can you find bad cases of early termination?

Notes

No error checking is done on the initial inputs. In particular, the bisection method doesn't check that the function has different signs at each end of the interval. The Newton and secant methods stop when $|f(x)| < 0.01$ . The bisection method stops when the interval size is smaller than 0.04.

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Java source code

(Other applets by James Stewart)