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.

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