- #1
dduardo
Staff Emeritus
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Can someone get me going in the right direction.
For the given function:
y[n] = (1/2)(y[n-1] + x[n]/y[n-1])
where x[n] = a * u[n] (u[n] is the unit step function)
and y[-1] = 1
prove that y[n] as n -> infinity is equal to sqrt(a)
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I know that this is the Newton-Raphson Method, but how do I go about analytically proving the above.
I've tried writing out a few terms and seeing if there is a pattern, but couldn't find anything.
The inside looks like a accumulator and tried to do a subsitution, but that didn't work.
Any help would be appreciated.
For the given function:
y[n] = (1/2)(y[n-1] + x[n]/y[n-1])
where x[n] = a * u[n] (u[n] is the unit step function)
and y[-1] = 1
prove that y[n] as n -> infinity is equal to sqrt(a)
-----------
I know that this is the Newton-Raphson Method, but how do I go about analytically proving the above.
I've tried writing out a few terms and seeing if there is a pattern, but couldn't find anything.
The inside looks like a accumulator and tried to do a subsitution, but that didn't work.
Any help would be appreciated.
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