Newton's Method

A brief description

The basic idea is that the function might be zero close to the point where a tangent line to the function intersects the horizontal axis. So we use the intersection of the horizontal axis with the tangent line (at the current estimate) as our next estimate. As the examples provided here show, Newton's method sometimes works very efficiently, but other times it fails to work at all. More sophisticated methods generally combine Newton's method with other methods (like the biject method) to compensate for its deficiencies while taking advantage of its strengths.

Newton's iteration formula (the algebraic equation that shows how to get a new estimate from a current estimate) is easily derived from simple facts about slopes of lines and the geometric meaning of the derivative. It can also be found in most calculus text books.

Usage Notes

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