Jsun Yui Wong
The following computer program seeks to solve the elliptical equation of Example 10.1 of Yang [21, pp.118-119].
0 DEFDBL A-Z
3 DEFINT J, K
4 DIM X(32768), A(32768), P(32768), K(32768)
5 FOR JJJJ = -32000 TO 32000
14 RANDOMIZE JJJJ
16 M = -1D+50
18 H = .25
91 FOR KK = 0 TO 4
94 IF RND < .5 THEN A(KK) = 1 - RND ELSE A(KK) = 1 + RND
95 NEXT KK
128 FOR I = 1 TO 10000 STEP 1
129 FOR K = 0 TO 4
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 4)
183 R = (1 - RND * 2) * A(B)
188 IF RND < .2 THEN X(B) = A(B) + RND * R ELSE IF RND < .25 THEN X(B) = A(B) + RND ^ 3 * R ELSE IF RND < .333 THEN X(B) = A(B) + RND ^ 5 * R ELSE IF RND < .5 THEN X(B) = A(B) + RND ^ 7 * R ELSE X(B) = A(B) + RND ^ 9 * R
199 NEXT IPP
566 X(0) = 1
577 X(4) = 0
586 FOR J44 = 2 TO 3
611 X(J44) = .0625 - X(J44 - 2) + 2 * X(J44 - 1)
613 NEXT J44
714 PNEW = X(2) - 2 * X(3) - .0625
999 P = -ABS(PNEW)
1451 IF P <= M THEN 1670
1657 FOR KEW = 0 TO 4
1658 A(KEW) = X(KEW)
1659 NEXT KEW
1661 M = P
1670 NEXT I
1890 REM IF M < -.1 THEN 1999
1911 PRINT A(0), A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [19]. Copied by hand from the screen, the computer program’s complete output through JJJJ= -31997 is shown below.
1 .6562499999994446 .3749999999988891
.1562499999983337 0 -2.221778316879863D-12
-32000
1 .6562500000000195 .3750000000000391
.1562500000000586 0 -7.815970093361102D-14
-31999
1 .6562500000000126 .3750000000000251
.1562500000000376 0 -5.018208071305708D-14
-31998
1 .6562500000000527 .3750000000001055
.1562500000001582 0 -2.109423746787797D-13
-31997
Above there is no rounding by hand; it is just straight copying by hand from the screen.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and with qb64v1000-win [19], the wall-clock time for obtaining the output through JJJJ= -31997 was three seconds, not including "Creating .EXE file..." time.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[19] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
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Solve a 19X19 System of Nonlinear Equations, Fourth Edition.
http://myblogsubstance.typepad.com/substance/2016/04/-the-domino-method-of-nonlinear-integercontinuousdiscrete-programming-seeking-to-solve-a-19×19-syste.html.
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