HP 15c - Manual (Page 239)

Appendix D: A Detailed Look at _ 239
Counting Iterations
While searching for a root, _ typically samples your function at least
a dozen times. Occasionally, _ may need to sample it one hundred
times or more. (However, _ will always stop by itself.) Because your
function subroutine is executed once for each estimate that is tried, it can
count and limit the number of iterations. An easy way to do this is with an
I instruction to accumulate the number of iterations in the Index
register (or other storage register).
If you store an appropriate number in the register before using _, your
subroutine can interrupt the _ algorithm when the limit is exceeded.
Specifying a Tolerance
You can shorten the time required to find a root by specifying a tolerable
inaccuracy for your function. Your subroutine should return a function
value of zero if the calculated function value is less than the specified
tolerance. This tolerance that you specify should correspond to a value that
is negligible for practical purposes or should correspond to the accuracy of
the computation. This technique eliminates the time required to define the
estimate more accurately than is justify by the problem. The example on
page 224 uses this method.)
For Advanced Information
In the HP-15C Advanced Functions Handbook, additional, advanced
techniques and applications for using _ are presented. These topics
include:
 Using _ with polynomials.
 Solving a system of equations.
 Finding local extremes of a function.
 Using _ for financial problems.
 Using _ in Complex mode.
 Solving an equation for its complex roots.