Re: A question on Newton's Method

David M wrote:
> [...] someone pointed out that using the quadratic equation is not
> exactly stable when it comes to computers. [...]

It should not be necessary to use Newton's method. Cancellation in
the usual quadratic formula can be avoided by recognizing that

-b +- sqrt(b^2 - 4ac) -2c
--------------------- = --------------------.
2a b +- sqrt(b^2 - 4ac)


If b is positive then get the two roots as

-b - sqrt(b^2 - 4ac) -2c
-------------------- and -------------------.
2a b + sqrt(b^2 - 4ac)


If b is negative then use

-b + sqrt(b^2 - 4ac) -2c
-------------------- and -------------------.
2a b - sqrt(b^2 - 4ac)

.