HP 15c - Manual (Page 220)

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Appendix D
A Detailed Look at _
Section 13, Finding the Roots of an Equation, includes the basic
information needed for the effective use of the _ algorithm. This
appendix presents more advanced, supplemental considerations regarding
_.
How _ Works
You will be able to use _ most effectively by having a basic
understanding of how the algorithm works.
In the process of searching for a zero of the
specified function, the algorithm uses the
value of the function at two or three
previous estimates to approximate the shape
of the function’s graph. The algorithm uses
this shape to intelligently ―predict‖ a new
estimate where the graph might cross the x-
axis. The function subroutine is then
executed, computing the value of the
function at the new estimate. This procedure is performed repeatedly by the
_ algorithm.
If any two estimates yield function values
with opposite signs, the algorithm presumes
that the function's graph must cross the x-
axis in at least one place in the interval
between these estimates. The interval is
systematically narrowed until a root of the
equation is found.
A root is successfully found either if the
computed function value is equal to zero or
if two estimates, differing by one unit in their last significant digit, give
function values having opposite signs. In this case, execution stops and the
estimate is displayed.