Using the preceding computer program as a template to solve simultaneously 2*x+y=5-2z^2, y^3+4*z=4, and x*y + z= e^z, second edition
Jsun Yui Wong
The computer program listed below aims to solve the following system of nonlinear equations from Google search [34]:
2*x+y=5-2*z^2
y^3+4*z=4
x*y + z= e^z.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)
85 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
114 REM A(1) = RND * 20
116 A(2) = RND * 20
119 REM A(3) = RND * 2
128 FOR i = 1 TO 10000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 3)
140 B = 1 + FIX(RND * 3)
144 IF RND < .5 THEN 160 ELSE GOTO 167
160 r = (1 - RND * 2) * A(B)
164 X(B) = A(B) + (RND ^ (RND * 15)) * r
165 GOTO 168
167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)
168 NEXT IPP
222 X(3) = (4 - X(2) ^ 3) / 4
224 X(1) = (5 - 2 * X(3) ^ 2 - X(2)) / 2
333 FOR J44 = 1 TO 3
335 IF X(J44) < 0 THEN 1670
337 NEXT J44
459 REM REM PD1 = -ABS(X(1) ^ 5 + X(2) ^ 5 - 464)
460 PD1 = -ABS(X(1) * X(2) + X(3) - 2.718281828 ^ X(3))
466 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 3
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1777 IF M < -1 THEN 1999
1904 PRINT A(1), A(2), A(3), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31998 is shown below:
1.422469 .9753885 .7680081 -8.071313E-09
-32000
1.422469 .9753885 .7680081 -8.071313E-09
-31999
1.422469 .9753885 .7680081 -8.071313E-09
-31998
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31998 was 3 seconds, counting from "Starting program...".
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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