Jsun Yui Wong

The computer program listed below seeks to solve simultaneously the following six equations:

X(4) +X(1) - .001 + X(2)=0,

X(5) - 55 + X(6)=0,

X(1) + X(2) + X(3) + 2 * X(5) + X(6) - 110.001 =0,

X(1) - .1 * X(2)=0,

X(1) - 10 ^ 4 * X(3)*X(4)=0,

X(5) - 55 * 10 ^ 14 * X(3) * X(6) =0.

These equations are Hiebert's six equations in Rheinboldt [79, p. 3].

One notes line 162, which is 162 IF RND < .16666 THEN X(j) = A(j) - FIX(1 + RND * 2.3) ELSE IF RND < .33333 THEN X(j) = A(j) + FIX(1 + RND * 2.3) ELSE IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 20.3) ELSE IF RND < .66666 THEN X(j) = A(j) + FIX(1 + RND * 20.3) ELSE IF RND < .83333 THEN X(j) = A(j) - FIX(1 + RND * 200.3) ELSE X(j) = A(j) + FIX(1 + RND * 200.3).

One also notes line 236, which is 236 X(J44) = ABS(X(J44)) .

0 DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

83 RANDOMIZE JJJJ

87 M = -4E+299

120 FOR J44 = 1 TO 6

121 A(J44) = FIX(RND * 6)

122 REM A(J44) = (RND * 2)

123 NEXT J44

128 FOR I = 0 TO FIX(RND * 2000000)

129 FOR KKQQ = 1 TO 6

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

135 FOR IPP = 1 TO FIX(1 + RND * 3.3)

143 j = 1 + FIX(RND * 6)

154 IF RND < .5 THEN GOTO 156 ELSE GOTO 162

156 REM

157 R = (1 - RND * 2) * (A(j))

160 X(j) = A(j) + (RND ^ (RND * 30)) * R

161 GOTO 169

162 IF RND < .16666 THEN X(j) = A(j) - FIX(1 + RND * 2.3) ELSE IF RND < .33333 THEN X(j) = A(j) + FIX(1 + RND * 2.3) ELSE IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 20.3) ELSE IF RND < .66666 THEN X(j) = A(j) + FIX(1 + RND * 20.3) ELSE IF RND < .83333 THEN X(j) = A(j) - FIX(1 + RND * 200.3) ELSE X(j) = A(j) + FIX(1 + RND * 200.3)

169 NEXT IPP

233 FOR J44 = 1 TO 6

236 X(J44) = ABS(X(J44))

239 NEXT J44

1123 X(1) = .1 * X(2)

1125 X(4) = -X(1) + .001 - X(2)

1128 X(3) = (X(1)) / (10 ^ 4## * X(4))

1129 X(5) = 55 - X(6)

1210 y2 = X(5) - 55 * 10 ^ 14## * X(3) * X(6)

1211 y1 = X(1) + X(2) + X(3) + 2 * X(5) + X(6) - 110.001##

1245 P = -ABS(y1) - ABS(y2)

1251 IF P <= M THEN 1670

1420 M = P

1444 FOR KLX = 1 TO 6

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1458 yyy1 = y1

1459 yyy2 = y2

1557 GOTO 128

1670 NEXT I

1894 IF M < -.0001 THEN 1999

1924 PRINT A(1), A(2), A(3), A(4), A(5)

1925 PRINT A(6), M, JJJJ, yyy1, yyy2

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [107]. The complete output of a single run through JJJJ= -31113 is shown below:

7.888091725752713D-05 7.888091725752713D-04 5.9618298552122233D-05

1.323099101672016D-04 54.99999999983227

1.677337368362975D-10 -7.26917793451784D-05 -31668

-7.269177934363796D-05 -1.540434446667405D-15

.

.

.

8.280864421154111D-05 8.28086442115411D-04 9.293386952305496D-05

8.910491367304793D-05 54.99999999998924

1.076033963860683D-10 -3.828848240950561D-06 -31113

3.828848239378901D-06 1.571659469234987D-15

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Processor Intel (R) Core (TM) 2 Duo CPU E8400 @ 3.0 GHz 3.0 GHz, 4.00 GB of RAM (3.9 GB usable), 64-bit Operating System, and QB64v1000-win [107], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31113 was 28 minutes, counting from "Starting program...".

**Acknowledgement**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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