Jsun Yui Wong
The computer program listed below seeks to solve the instance of n=11019 of the following problem from Montazeri, Soleymani, Shateyi, and Motsa [74, p. 11]:
X(i) * X(i + 1) – 1=0, i=1, 2, 3,…, n-1,
X(n) * X(1) – 1=0, for odd n.
0 DEFDBL A-Z
1 DEFINT K
2 DIM B(99), N(99), A(11100), H(99), L(99), U(99), X(11100), 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 11019
121 A(J44) = 1 + FIX(RND * 6)
122 REM A(J44) = (RND)
123 NEXT J44
128 FOR I = 0 TO FIX(RND * 300000)
129 FOR KKQQ = 1 TO 11019
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 10)
143 J = 1 + FIX(RND * 11019.5)
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 REM 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)
163 IF RND < .5 THEN X(J) = A(J) – FIX(1 + RND * .3) ELSE X(J) = A(J) + FIX(1 + RND * .3)
169 NEXT IPP
170 FOR J44 = 1 TO 11019
171 REM X(J44) = INT(X(J44))
172 IF X(J44) < .01## THEN 1670
173 NEXT J44
194 FOR J44 = 1 TO 11018
197 X(J44 + 1) = 1 / X(J44)
199 NEXT J44
1151 SUMM = 0
1154 FOR J44 = 1 TO 11018
1157 SUMM = SUMM – ABS(X(J44) * X(J44 + 1) – 1)
1159 NEXT J44
1166 SUMMM = SUMM – ABS(X(11019) * X(1) – 1)
1169 P = SUMMM
1351 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 11019
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1688 IF M < -.0000001 THEN 1999
1924 PRINT A(1), A(2), A(3), A(4), A(5)
1925 PRINT A(5011), A(5012), A(5013), A(5014), A(5015)
1928 PRINT A(6011), A(6012), A(6013), A(6014), A(6015)
1929 PRINT A(8011), A(8012), A(8013), A(8014), A(8015)
1933 PRINT A(11016), A(11017), A(11018), A(11019), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [119]. The output specified by line 1924 through line 1933 of a single run through
JJJJ= -31980 is shown below:
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002 .9999999999999982
1.000000000000002 -3.552713678800501D-15 -31998
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
-31997
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
-31982
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
-31981
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
-31980
In accordance with line 1924 through 1933, only 24 values of the 11019 values of the variables are shown above.
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 [119], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31980 was 66 minutes, counting from “Starting program…”.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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Solving a Nonlinear Programming Problem in 11019 Variables
Jsun Yui Wong
The computer program listed below seeks to solve the instance of n=11019 of the following problem from Montazeri, Soleymani, Shateyi, and Motsa [74, p. 11]:
X(i) * X(i + 1) – 1=0, i=1, 2, 3,…, n-1,
X(n) * X(1) – 1=0, for odd n.
0 DEFDBL A-Z
1 DEFINT K
2 DIM B(99), N(99), A(11100), H(99), L(99), U(99), X(11100), 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 11019
121 A(J44) = 1 + FIX(RND * 6)
122 REM A(J44) = (RND)
123 NEXT J44
128 FOR I = 0 TO FIX(RND * 300000)
129 FOR KKQQ = 1 TO 11019
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 10)
143 J = 1 + FIX(RND * 11019.5)
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 REM 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)
163 IF RND < .5 THEN X(J) = A(J) – FIX(1 + RND * .3) ELSE X(J) = A(J) + FIX(1 + RND * .3)
169 NEXT IPP
170 FOR J44 = 1 TO 11019
171 REM X(J44) = INT(X(J44))
172 IF X(J44) < .01## THEN 1670
173 NEXT J44
194 FOR J44 = 1 TO 11018
197 X(J44 + 1) = 1 / X(J44)
199 NEXT J44
1151 SUMM = 0
1154 FOR J44 = 1 TO 11018
1157 SUMM = SUMM – ABS(X(J44) * X(J44 + 1) – 1)
1159 NEXT J44
1166 SUMMM = SUMM – ABS(X(11019) * X(1) – 1)
1169 P = SUMMM
1351 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 11019
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1688 IF M < -.0000001 THEN 1999
1924 PRINT A(1), A(2), A(3), A(4), A(5)
1925 PRINT A(5011), A(5012), A(5013), A(5014), A(5015)
1928 PRINT A(6011), A(6012), A(6013), A(6014), A(6015)
1929 PRINT A(8011), A(8012), A(8013), A(8014), A(8015)
1933 PRINT A(11016), A(11017), A(11018), A(11019), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [119]. The output specified by line 1924 through line 1933 of a single run through
JJJJ= -31980 is shown below:
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
1.000000000000002 .9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002
.9999999999999982 1.000000000000002 .9999999999999982
1.000000000000002 -3.552713678800501D-15 -31998
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
-31997
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
-31982
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
-31981
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
-31980
In accordance with line 1924 through 1933, only 24 values of the 11019 values of the variables are shown above.
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 [119], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31980 was 66 minutes, counting from “Starting program…”.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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[115] Eric W. Weisstein, “Diophantine Equation–5th Powers.” https://mathworld.wolfram.com/DiophantineEquation5thPowers.html.
[116] Eric W. Weisstein, “Diophantine Equation–10th Powers.” https://mathworld.wolfram.com/DiophantineEquation10thPowers.html.
[117] Eric W. Weisstein, “Diophantine Equation–9th Powers.” https://mathworld.wolfram.com/DiophantineEquation9thPowers.html.
[118] Rick Wicklin (2018), Solving a system of nonlinear equations with SAS.
blogs.sas.com>iml>2018/02/28. One can directly read this on Google.
[119] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
[120] Jsun Yui Wong (2014, March 13). The Domino Method Applied to a System of Four Simultaneous Nonlinear Equations. Retrieved from http://myblogsubstance.typepad.com/substance/2014/03.
[121] Zhongkai Xu, Way Kuo, Hsin-Hui Lin (1990). Optimization Limits in Improving System Reliability. IEEE Transactions on Reliability, Vol. 39, No. 1, 1990 April, pp. 51-60.
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