(In reply to
Iteration plus guess by Larry)
Iteration could be continued until it settles down (could also use a limit on the absolute value difference instead of inequality):
a=0; prev=-1;
while prev~=a
prev=a;
a=sqrt(4-sqrt(5-a))
end
b=0; prev=-1;
while prev~=b
prev=b;
b=sqrt(4+sqrt(5-b))
end
c=0; prev=-1;
while prev~=c
prev=c;
c=sqrt(4-sqrt(5+c))
end
d=0; prev=-1;
while prev~=d
prev=d;
d=sqrt(4+sqrt(5+d))
end
a*b*c*d
a =
1.32813102610406
a =
1.44353311628272
a =
1.45400834933892
a =
1.45496379259351
a =
1.45505097726045
a =
1.455058933229
a =
1.45505965924739
a =
1.4550597254999
a =
1.45505973154574
a =
1.45505973209745
a =
1.4550597321478
a =
1.45505973215239
a =
1.45505973215281
a =
1.45505973215285
a =
1.45505973215285
a =
1.45505973215285
a =
1.45505973215286
a =
1.45505973215286
b =
2.49721204095683
b =
2.36262993600061
b =
2.37149703192152
b =
2.37092088725225
b =
2.37095835633226
b =
2.37095591970525
b =
2.37095607816053
b =
2.3709560678561
b =
2.3709560685262
b =
2.37095606848262
b =
2.37095606848546
b =
2.37095606848527
b =
2.37095606848528
b =
2.37095606848528
b =
2.37095606848528
c =
1.32813102610406
c =
1.21836871576504
c =
1.22732810669003
c =
1.22659630614774
c =
1.22665607602821
c =
1.22665119429492
c =
1.22665159301265
c =
1.2266515604472
c =
1.226651563107
c =
1.22665156288976
c =
1.2266515629075
c =
1.22665156290605
c =
1.22665156290617
c =
1.22665156290616
c =
1.22665156290616
c =
1.22665156290616
d =
2.49721204095683
d =
2.59578576366798
d =
2.59923937188159
d =
2.59935988130874
d =
2.5993640857422
d =
2.59936423242926
d =
2.59936423754697
d =
2.59936423772552
d =
2.59936423773175
d =
2.59936423773197
d =
2.59936423773198
d =
2.59936423773198
d =
2.59936423773198
ans =
11
Edited on March 5, 2025, 3:43 pm
|
|
Posted by Charlie
on 2025-03-05 15:40:16 |
re: Iteration plus guess -- the iterative method
