## Quick Reference

An algorithmic method for constructing a sequence of approximations to a root of an equation. Suppose it is desired to solve the equation f(*x*)=0 and that *x*_{1} is an approximate value for the root of the equation. If we write f′(*x** _{n}*) for the value of the derivative of f(

*x*) (with respect to

*x*) evaluated at the point

*x*=

*x*

*, the sequence defined by usually converges to a root of the equation. It is based on constructing the tangent to the curve*

_{n}*y*=f(

*x*) at the point (

*x*

*, f(*

_{n}*x*

*), and taking*

_{n}*x*

*to be the*

_{n+1}*x*-coordinate of the point where this tangent cuts the

*x*-axis.

*Subjects:*
Probability and Statistics.

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