Iterative method to find square root of a matrix
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More numerically stable than babylonian method.
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Can make use of initial guess, as opposed to Denman beavers.
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Only matrix multiplications and suc. No inverses in the iteration.
Uses Newton's method. Step is calculated using Conjugate Gradient, truncated to one or a few iterations.
Want to solve [N,N] matrix-equation:
Newtons method:
This is all we need if we choose to use a matrix-free method like Conjugate Gradient to get the step in Newton's method. This inner iteration can be truncated after only a few iterations.