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  3. theorem 3 convergence of herons algorithm let a be a...

Question: theorem 3 convergence of herons algorithm let a be a...

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Theorem 3. (Convergence of Herons Algorithm). Let a be a positive real number, and choose an mtial estimate xo 0. Then the sequence (xm o defined by the iteration comverges to Va Proof. Let E-x Va be the error at step n of Herons algorithm. By the reasoning above we can always assume that x va and therefore that En 20.We compute En+1, the error at stepn +1, in terms of the current eror En. The plan is to show that the sequence of iterates En converges to zero. Form the error and relate it to the previous step through Herons method, After some algebra (left to you as a homework problem) we find that 2x Problem 1. In the convergence proof of Herons algorithm given in the notes, it is stated that after some algebra the error En+ is Do the algebra to derive this result. Hint: start by rewriting the equation as
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