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## Square Root by Iteration Method

Started by GWS, December 04, 2019, 01:08:50 PM

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#### GWS

##### December 04, 2019, 01:08:50 PM
Here's another oldie which is probably not really needed these days.

We have an inbuilt SQRT() function which is probably faster and more accurate.

However, it's interesting to see how the iteration is used.

Note that it needs Double precision to work correctly ..

`' Square Root by Iteration ..openconsolecls' Calculating a Square Root using Iteration ..def x,y,z:doubledef i:intsetprecision 10print' Example:z = 27 :' positive real number whose Square root is requiredprintprint "Square Root of ",z:print:print STRING\$(30, "_" )print:print:print "Iterations: ":printx = z/2 :' arbitrary start value for the iterationdo x = 0.5 * (x + z/x) print xuntil ((x*x - z)/z <= 1.e-11) :' the test for convergenceprintprint "The Square Root of ",z, " is  ", x' Compare with the inbuilt Sqrt() function ..print:printprint "Using the CB Sqrt() Function, the result is .. ":printprint sqrt(z)print:print STRING\$(30, "_" )do:until inkey\$<>""closeconsoleend`
Best wishes,

Graham

Tomorrow may be too late ..