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Appendix D: A Detailed Look at _ 221

As discussed in section 13, page 186, the occurrence of other situations in

the iteration process indicates the apparent absence of a function zero. The

reason is that there is no way to logically predict a new estimate that is

likely to have a function value closer to zero. In such cases, Error 8 is

displayed.

You should note that the initial estimates you provide are used to begin the

"prediction" process. By permitting more accurate predictions than might

otherwise occur, properly chosen estimates greatly facilitate the

determination of the root you seek.

The _ algorithm will always find a root provided one exists

(within the overflow bounds), if any one of four conditions are met:



Any two estimates have function

values with opposite signs.



The function is monotonic, meaning

that f(x) either always decreases or

else always increases as x is

increased.

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HP 15C Bedienungsanleitung Seite 221