Jsun Yui Wong
The computer program listed
below seeks to solve simultaneously the following system of nonlinear
equations:
(COS(X(2)) - X(3) *
SIN(X(1))) =0
(X(3) ^ X(1) - 1 / X(2)) =0
(2.718281828 ^ X(1) - X(2) *
X(3) ^ 2) =0
where X(1) through X(3) are continuous variables.
The three equations above are based on Expression 71 in Moreno, Lopez, and
Martinez [62, Example 2].
0 DEFDBL A-Z
1 DEFINT K
2 DIM B(99), N(99), A(2002),
H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99),
HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20),
WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)
81 FOR JJJJ = -32000 TO
32000
83 RANDOMIZE JJJJ
87 M = -4E+299
120 FOR J44 = 1 TO 3
121 A(J44) = FIX(RND * 3)
122 REM A(J44) = (RND * 2)
123 NEXT J44
128 FOR I = 0 TO FIX(RND * 500000)
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 3.3)
143 j = 1 + FIX(RND * 3)
154 IF RND < .5 THEN GOTO 156
ELSE GOTO 162
156 REM
157 R = (1 - RND * 2) * (A(j))
160 X(j) = A(j) + (RND ^ (RND *
15)) * R
161 GOTO 169
162 IF RND < .5 THEN X(j) = A(j)
- FIX(1 + RND * 3.3) ELSE X(j) = A(j) + FIX(1 + RND * 3.3)
169 NEXT IPP
171 FOR J44 = 1 TO 3
172 IF X(J44) < 0 THEN 1670
174 IF X(J44) > 10 THEN 1670
175 NEXT J44
1125 P = -ABS(COS(X(2)) - X(3) *
SIN(X(1))) - ABS(X(3) ^ X(1) - 1 / X(2)) - ABS(2.718281828 ^ X(1) - X(2) * X(3)
^ 2)
1221 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 3
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1894 IF M < -.0000009 THEN 1999
1923 PRINT A(1), A(2), A(3), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program
was run with QB64v1000-win [104]. The
complete output of a single run through
JJJJ= -31989 is shown below:
.4951043997686503 .8496868533639608 1.389572161712821
-1.40103073220947D-07 -31997
.4951041722089981 .8496874547348392 1.389571511868924
-4.675691889858007D-07 -31989
Above there is no rounding
by hand; it is just straight copying by hand from the monitor screen. On a
personal computer with Processor Intel (R) Core (TM) 2 Duo CPU E8400 @ 3.0
GHz 3.0 GHz, 4.00 GB of RAM (3.9 GB
usable), 64-bit Operating System, and
QB64v1000-win [104], the wall-clock time (not CPU time) for obtaining the
output through JJJJ = -31989 took 15 seconds, counting from
"Starting program...". One can
compare the computational results above with those in Moreno et al. [62, Table
2 ].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom
Clark.
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