Jsun Yui Wong
The computer program listed
below seeks to solve the following system of three nonlinear equations from
Burden, Faires, and Burden [17, Exercise Set 10.2, Exercise 9, p. 657]:
3 * X(1) - COS(X(2) * X(3)) - 1 / 2 =0,
X(1) ^ 2 - 625 * X(2) ^ 2 -
1 / 4 =0,
EXP(-X(1) * X(2)) + 20 *
X(3) + (10 * 3.141592654 - 3) / 3=0.
One notes line 1111, which
is 1111 P = -ABS(3 * X(1) - COS(X(2) * X(3)) - 1 / 2) - ABS(X(1) ^ 2 - 625 *
X(2) ^ 2 - 1 / 4) - ABS(EXP(-X(1) * X(2)) + 20 * X(3) + (10 * 3.141592654 - 3)
/ 3), which very much resembles the given system of equations.
0 DEFDBL A-Z
2 REM DEFINT K
3 DIM B(99), N(99),
A(100255), H(99), L(99), U(99), X(100250), D(111), P(511), PS(33), J(30003),
J44(30003), KKQQ(30003), KLX(30003), W(10111)
12 FOR JJJJ = -32000 TO
32000 STEP .01
13 RANDOMIZE JJJJ
16 M = -1D+37
18 FOR J44 = 1 TO 3
19 A(J44) = -1 + RND * 2
25 NEXT J44
128 FOR I = 1 TO 10000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO (1 + FIX(RND * 4))
148 J = 1 + FIX(RND * 3)
154 IF RND < .5 THEN GOTO 157
ELSE GOTO 164
157 R = (1 - RND * 2) * (A(J))
160 X(J) = A(J) + (RND ^ (RND *
30)) * R
161 GOTO 174
164 IF RND < .5 THEN X(J) = A(J)
- FIX(1 + RND * .3) ELSE X(J) = A(J) + FIX(1 + RND * .3)
174 NEXT IPP
1111 P = -ABS(3 * X(1) - COS(X(2) *
X(3)) - 1 / 2) - ABS(X(1) ^ 2 - 625 * X(2) ^ 2 - 1 / 4) - ABS(EXP(-X(1) * X(2))
+ 20 * X(3) + (10 * 3.141592654 - 3) / 3)
1119 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 3
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1671 IF M < -.000001 THEN GOTO 1999
1914 PRINT A(1), A(2), A(3), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program
was run with qb64v1000-win [120]. The
complete output of one run through JJJJ=-31999.9000000002 is shown below:
.49999999999999483 1.064242821587623D-06 -.5235987490606032
-7.079347259504685D-10 -32000
.4999999999976782 7.12844688533392D-06 -.5235985974558094
-3.176154466271234D-08 -31999.96000000001
.5 -8.937340003220426D-10 -.52359877568901
-4.992208903209505D-16 -31999.91000000001
.4999999999631051 -2.841576431708798D-05 -.5235994860658212
-5.046966834537187D-07 -31999.90000000002
Above there is no rounding
by hand; it is just straight copying by hand from the monitor screen.
The system properties of the
computer system used include Intel Core 2 Duo CPU E8400 @ 3.00GHz 3.00GHz, 4.00GB of RAM, and qb64v1000-win
[120]. The wall-clock time (not CPU
time) for obtaining the output shown above was 4 seconds, counting from
“Starting program…”. The computational
results shown above are compatible with those in Burden, Faires, and Burden
[17, Exercise Set 10.2, Exercise 9, p. 872].
Acknowledgement
I would like to acknowledge
the encouragement of Roberta Clark and Tom Clark.
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