Jsun Yui Wong
Here the nonlinear system of
interest is:
3 * X(1) ^ 3 + 2 * X(2) - 5 + SIN(X(1)
- X(2)) * SIN(X(1) + X(2)) =0,
-X(J44 - 1) * EXP(X(J44 - 1) - X(J44))
+ X(J44) * (4 + 3 * X(J44) ^ 2) + 2 * X(J44 + 1) + SIN(X(J44) - X(J44 + 1)) *
SIN(X(J44) + X(J44 + 1)) - 8 =0, J44 = 2 TO 14999,
-X(14999) * EXP(X(14999) - X(15000)) +
4 * X(15000) - 3 =0.
This nonlinear system of
interest is based on the nonlinear system 12 in La Cruz and Raydan [58, p. 598,
Appendix:Test Functions]:
The computer program below
tries to answer what if there is a solution vector with all integers. Then one can have line 19 and line 224, which
are 19 A(J44) = INT(-3 + RND * 6) and 224 X(J44) = INT(X(J44)), respectively.
0 DEFDBL A-Z
2 REM DEFINT K
3 DIM B(99), N(99),
A(200111), H(99), L(200111), U(99), X(200111), D(111), P(511), PS(33),
J(200111), J44(200111), KKQQ(200111), KLX(200111), W(200111), LSUM(200111)
12 FOR JJJJ = -32000 TO
32000 STEP .01
13 RANDOMIZE JJJJ
16 M = -1D+37
18 FOR J44 = 1 TO 15000
19 A(J44) = INT(-3 + RND * 6)
25 NEXT J44
128 FOR I = 1 TO 50000
129 FOR KKQQ = 1 TO 15000
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO (1 + FIX(RND * 4))
148 J = 1 + FIX(RND * 15100)
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
222 FOR J44 = 1 TO 15000
224 X(J44) = INT(X(J44))
226 NEXT J44
1012 L(1) = 3 * X(1) ^ 3 + 2 * X(2) - 5
+ SIN(X(1) - X(2)) * SIN(X(1) + X(2))
1020 FOR J44 = 2 TO 14999
1026 L(J44) = -X(J44 - 1) *
EXP(X(J44 - 1) - X(J44)) + X(J44) * (4 + 3 * X(J44) ^ 2) + 2 * X(J44 + 1) +
SIN(X(J44) - X(J44 + 1)) * SIN(X(J44) + X(J44 + 1)) - 8
1027 NEXT J44
1046 L(15000) = -X(14999) *
EXP(X(14999) - X(15000)) + 4 * X(15000) - 3
1048 SUMM = 0
1051 FOR J44 = 1 TO 15000
1055 SUMM = SUMM + ABS(L(J44))
1057 NEXT J44
1113 P = -ABS(SUMM)
1119 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 15000
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1913 PRINT A(1), A(2), A(3), A(4), A(5)
1914 PRINT A(6), A(7), A(8), A(14993),
A(14994)
1915 PRINT A(14995), A(14996), A(14997),
A(14998), A(14999)
1916 PRINT A(15000), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program
was run with qb64v1000-win [120]. The
complete output of one run through JJJJ=-31999.99 is shown below:
1 1
1 1 1
1 1
1 1 1
1 1
1 1 1
1 -11.71828182845905 -32000
1 1
1 1 1
1 1
1 1 1
1 1
1 1 1
1 0 -31999.99
One notes that only 16
values of the 15000 values of A(1) through A(15000) are shown above, in
accordance with line 1913 through line 1916.
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 3 hours and 44 minutes, counting
from “Starting program…”.
Acknowledgement
I would like to acknowledge
the encouragement of Roberta Clark and Tom Clark.
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