calvin mccarter

The Newton Schulz method is well-known, and the proof of convergence is widely available on the internet. Yet the derivation of the method itself is more obscure. Here it is:

We seek the zero of , defined as follows:
.

The derivative of at , applied to matrix , operates on as follows:

We can then prove that at , applied to matrix , operates on as follows:
.

To see this, notice that

The Newton method for root finding has at each iterate:
.

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This was originally published here: https://calvinmccarter.wordpress.com/2021/11/18/the-newton-schulz-iteration-for-matrix-inversion/

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