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:
opposite signs.
The function is monotonic,
meaning that f (x)
always increases as x
increased.
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