A general-purpose computer program for solving nonlinear systems of equations
Jsun Yui Wong
Similar to the computer programs of the preceding papers, the computer program listed below seeks to solve the following system of 50 nonlinear equations from Sharma and Gupta [80, p. 7, Problem 5]:
X(i)^2 * X(i+1) - 1 = 0, (i=1, 2,..., 49)
X(50)^2* X(1) - 1 = 0.
0 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
116 REM
118 A(1) = INT(0 + RND * 10)
128 FOR i = 1 TO 1500000
129 FOR KKQQ = 1 TO 50
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 50)
140 B = 1 + FIX(RND * 50)
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
231 FOR J44 = 2 TO 50
234 X(J44) = 1 / (X(J44 - 1)) ^ 2
239 NEXT J44
333 REM
334 FOR J44 = 1 TO 50
335 IF X(J44) < 0 THEN 1670
337 NEXT J44
461 REM
463 PD1 = -ABS(X(50) ^ 2 * X(1) - 1)
466 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 50
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1904 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), A(10), A(11), A(12), A(13), A(14), A(15), A(16), A(17), A(18), A(19), A(20), A(21), A(22), A(23), A(24), A(25), A(26), A(27), A(28), A(29), A(30), A(31), A(32), A(33), A(34), A(35), A(36), A(37), A(38), A(39), A(40), A(41), A(42), A(43), A(44), A(45), A(46), A(47), A(48), A(49), A(50), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its output of one run through
JJJJ= -31989 is summarized below:
4 .0625 256 .0000152587890625
.
.
.
-1 -32000
.
.
.
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
0 -31989
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 = -31989 was 9 minutes, 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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