Jsun Yui Wong
The computer program listed below seeks to solve the following system of nonlinear equations taken from Faires and Burden [3, p. 357]; this system can also be found in Burden and Faires [5, p. 653]:
4*X(1) - X(2) +X(3) = X(1)*X(4)
-X(1)+3*X(2)-2*X(3) = X(2)*X(4)
X(1)-2*X(2)+3*X(3) = X(3)*X(4)
X(1)^2+X(2)^2+X(3)^2 = 1
While line 128 of the preceding paper is 128 FOR I=1 TO 10000, line 128 here is
128 FOR I=1 TO 1000.
0 DEFDBL A-Z
1 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),PLHS(44),LB(22),UB(22),PX(44),J44(44),PN(22),NN(22)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-3D+30
110 FOR J44=1 TO 4
112 A(J44)=-5+(RND*10)
113 NEXT J44
128 FOR I=1 TO 1000
129 FOR KKQQ=1 TO 4
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*4)
150 R=(1-RND*2)*A(B)
155 REM IF RND<.5 THEN 160 ELSE 167
160 X(B)=(A(B) +RND^6*R)
165 GOTO 168
167 IF RND<.5 THEN X(B)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1)
168 NEXT IPP
211 X(2)=4#*X(1)+X(3)-X(1)*X(4)
301 N(2)=-X(1)+3#*X(2)-2#*X(3)-X(2)*X(4)
303 N(3)=X(1)-2#*X(2)+3#*X(3)-X(3)*X(4)
311 N(4)=X(1)^2#+X(2)^2#+X(3)^2#-1#
322 PD1=-ABS(N(4)) -ABS(N(2)) -ABS(N(3))
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 4
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-.000001 THEN 1999
1904 PRINT A(1),A(2),A(3)
1917 PRINT A(4),M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. Only distinct solutions through JJJJ=-31882 are showm below. What follows is a hand copy from the computer-monitor screen; immediately below there is no rounding by hand.
.81649658090046104 .4082482904965245 -.4082482904450159
2.999999999995477 -1.372581215353108D-10 -31999
-.8164965809190948 -.4082482904604736 .4082482904847439
2.999999999968006 -7.855482930807512D-11 -31998
3.719831440763078D-18 .7071067811866495 .7071067811866495
.9999999999999744 -3.247263569150505D-13 -31987
-.577350271681154 .5773502716751747 -.5773502716710746
5.999999999972186 -8.660539702054493D-09 -31978
-3.854485064170178D-19 -.7071067811866182 -.7071067811866182
1.000000000000021 -2.29621877068098D-13 -31975
.5773502704478668 -.5773502704381253 .5773502704420585
5.999999999973067 -4.38736860730593D-09 -31882
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output through JJJJ=-31882 was 120 seconds.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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