A very general computer program for solving simultaneously nonlinear/linear systems of equations

A very general computer program for solving simultaneously nonlinear/linear 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 of nonlinear equations from Sharma and Gupta [79, p. 9, Problem 3]:
10 * X(1) + SIN(X(1) + X(2)) - 1=0
8 * X(2) - COS(X(3) - X(2)) ^ 2 - 1=0
12 * X(3) + SIN(X(3)) - 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
115 FOR J44 = 1 TO 3
116 A(J44) = -0 + RND * 2

122 NEXT J44
128 FOR i = 1 TO 50000

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 * 13)) * 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

221 REM J45 = 1 + FIX(RND * 15)

224 REM IF RND < .5 THEN X(J45) = A(J45) - RND * .01 * A(J45) ELSE X(J45) = A(J45) + RND * .01 * A(J45)

333 FOR J44 = 1 TO 3

334 REM IF X(J44) < -10 THEN 1670

335 IF X(J44) < 0 THEN 1670
336 IF X(J44) > 1 THEN 1670

338 NEXT J44

340 REM SUMOF13 = X(1) + X(2) + X(3) + X(4) + X(5) + X(6) + X(7) + X(8) + X(9) + X(10) + X(11) + X(12) + X(13)

343 REM FOR J44 = 1 TO 13

351 LHS(1) = 10 * X(1) + SIN(X(1) + X(2)) - 1

352 LHS(2) = 8 * X(2) - COS(X(3) - X(2)) ^ 2 - 1

353 LHS(3) = 12 * X(3) + SIN(X(3)) - 1
377 REM NEXT J44

464 PD1 = -ABS(LHS(1) - 0) - ABS(LHS(2) - 0) - ABS(LHS(3) - 0)

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 < -2 * .000001 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:

6.897834917266645D-02 .2464424186091825 7.692891198753697D-02
-5.127083653466702D-15 -32000
6.897834917266855D-02 .2464424186091602 .076928911987537
-1.903428044520983D-13 -31999
6.897834917266661D-02    .246442418609183    7.692891198753694D-02
-8.5586919496000572D-16    -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 1 second, 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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