observed asymptotic behavior of each of these iterations. In section \[section: Examples\] we give some examples. In section \[section: Higher dimensional projective space\] we investigate the case for higher dimensional projective space.

It has recently come to the author’s attention that on Julien Keller’s web site [@keller] one can find a program to compute a Ricci flat metric on a particular $K3$ surface using the techniques of Donaldson on which this paper is based. More information can be found there. All computations and all graphs in this paper were done using the software Maple 9.

[**Acknowledgements.**]{} The author is grateful to Ben Weinkove for introducing him to this problem, and for answering endless questions. This paper would not have been possible without his help. The author would also like to thank the referee for many useful comments and suggestions which helped to improve this paper.

The $T$, $T_{\nu}$, and $T_K$ operators {#section: The T operators}
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Let $X$ be an $n$ dimensional complex projective manifold, and $L \rightarrow X$ an ample line bundle. In [@donaldson5] Donaldson examines three different actions on the space of Hermitian metrics on $\mathrm{H}^0(X, L^k)$: $T, T_{\nu}, T_K.$ We briefly recall how he defines each.

Given 