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Appendix D: A Detailed Look at _
If the algorithm terminates its search near a
local minimum of the function's magnitude,
clear the
display and observe the
Error 8
numbers in the X-, Y-, and Z-registers by
rolling down the stack. If the value of the
function saved in the Z-register is relatively
close to zero, it is possible that a root of
your equation has been found – the number
returned in the X-register may be a 10-digit
number very close to a theoretical root. You
can explore this potential minimum further by rolling the stack until the
returned estimates are back in the X- and Y-registers and then executing
_ again using these numbers as initial estimates. If an actual
minimum has been found,
will again be displayed and the number
Error 8
in the X-register will be approximately the same as before, but possibly
closer to the actual location of the minimum.
Of course, you may deliberately use _ to find the location of a local
minimum of the function's magnitude. However, in this case you must be
careful to confine the search in the region of the minimum. Remember,
_ tries hard to find a zero of the function.
If the algorithm stops searching and
displays
because it is working on a
Error 8
horizontal asymptote (when the value of
the function is essentially constant for a
large range of x), the estimates in X- and
Y-registers
usually
are
significantly
different from each other. The number in
the Z-register is the value of the potential
asymptote. If you execute _ again
using as initial estimates the numbers that
were returned in the X- and Y-registers, a
horizontal asymptote may again cause
Error 8
, but with numbers in the X-
and Y-registers that will differ from the previous numbers. The value of the
function in the Z-register would then be about the same as that obtained
previously.
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