HP 15c - Manual (Page 137)

Section 4: Using Matrix Operations 137
N Determines the maximum number of iterations that the program will attempt in each
of two procedures: the bounding search and the overall optimization procedure. That
is, the program halts if the bounding search finds no change of sign within N
iterations. Also, the program halts if the norm of the gradient is still too large at x
N
.
Each of these situations results in an Error 1 display. (They can be distinguished by
pressing −.) You can continue running the program if you desire.
The program requires that you enter a subroutine that evaluates f(x) and

f(x). This
subroutine must be labeled "E", use the vector x stored in matrix A, return the gradient in
matrix E, and place f(x) in the X-register.
In addition, the program requires an initial estimate x
0
of the desired critical point. This
vector must be stored in matrix A.
The program has the following characteristics:

The program searches for any point x where

f(x) = 0. Nothing prevents convergence
to a saddle-point, for example. In general, you must use other means to determine the
nature of the critical point that is found. (Also, this program does not address the
problem of locating a maximum or minimum on the boundary of the domain of f(x).)

You may adjust the convergence parameters after starting the program. In many cases,
this dramatically reduces the time necessary for convergence. Here are some helpful
hints:

If the program consistently enters the interval reduction phase after sampling only
one point u
1
, the initial step size may be too large. Try reducing the magnitude of d
to produce a more efficient search.

If the results of the bounding search look promising (that is, the slopes are
decreasing in magnitude), but then begin to increase in magnitude, the search may
have skipped past a critical point. Try reducing a to produce more close sampling;
you may have to increase N also.

You can replace ¦ at line 102 with © or perhaps delete it entirely if you have
no interest in the intermediate results.

For a function of n variables, the program requires 4n+1 registers devoted to matrices.
Keystrokes Display
|¥
Program mode.
´CLEARM 000-
´b8 001-42,21, 8 Routine to swap A and C using
E.
l>C 002-45,16,13
O>E 003-44,16,15
l>A 004-45,16,11
O>C 005-44,16,13
l>E 006-45,16,15
O>A 007-44,16,11