sqroot

this .m file will find successive approximations to the number sqrt(a)
using Newton's method.

type in your choice of the number a: 7
please type in your crude approximation to sqrt(a): 2.7

error =
   0.054248688935409   0.000544985231706   0.000000056117847   0.000000000000000
the square root of 7.00 is
ans =
   2.645751311064591
+++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++
clear all

x=1
x =
     1

n=1
n =
     1

fixed_point
rat =
  -0.055910758756935  -0.158529015192103  -0.158529015192103  -0.064450609345331
x =
   0.944089241243065   0.841470984807897   0.841470984807897   0.935549390654669

fixed_point
rat =
   0.213440751839848  -1.334527061151316  -0.944943137967995   0.087787714785998
x =
   0.932155606858048   1.053032245559427   0.991271889882499   0.929891418943678

fixed_point
rat =
   0.227496683288994  -1.273491097059171  -0.916685844572464   0.181094562559821
x =
   0.929440744615873   0.783610863509739   0.853951520696468   0.928866791031700

fixed_point
rat =
   0.230591425811820  -1.358031005344982  -0.955085330259390   0.189776342469133
x =
   0.928814720660568   1.149493453836111   0.985104190851850   0.928672340894173

fixed_point
rat =
   0.231300383242093  -1.254121027807776  -0.935133333242060   0.191356374740295
x =
   0.928669921079787   0.690632403599030   0.862458957245851   0.928635131620788

fixed_point
rat =
   0.231464124382053  -1.405489993178697  -0.961448182016276   0.191656495568375
x =
   0.928636405171610   1.335557017966715   0.980375994129300   0.928628000221848

fixed_point
rat =
   0.231502011773748  -1.225521631232276  -0.946165065961481   0.191713935349422
x =
   0.928628646171441   0.545187952544983   0.868807013148489   0.928626633033293

fixed_point
rat =
   0.231510782091528  -1.517668300232174  -0.965871742385128   0.191724944384068
x =
   0.928626849879244   1.744706028619674   0.976568339204558   0.928626370909143

fixed_point
rat =
   0.231512812505697  -1.184764319535624  -0.953573168159566   0.191727054884165
x =
   0.928626434014585   0.323559811448362   0.873810030112196   0.928626320652852

fixed_point
rat =
   0.231513282458981  -1.909313614333764  -0.969146092431661   0.191727459747364
x =
   0.928626337736393   3.036973631852477   0.973397843833943   0.928626311017341
quit