Chemistry Textbooks

Jack Simons has a couple of introductory chemistry textbooks on his website. They are An Introduction to Theoretical Chemistry and Quantum Mechanics in Chemistry (with Jeff Nichols).

Stochastic Matrix Inversion

I ran across this paper, A Monte Carlo algorithm for efficient large matrices inversion. There are a couple of techniques presented, one which is similar to the iterative Gauss-Seidel algorithm.

QMC methods often use a matrix to enforce antisymmetry conditions on a fermionic wavefunction. The determinant is needed for the wavefunction itself, and the inverse matrix is used for the local energy.

I wonder if a stochastic matrix algorithm would be useful in the QMC calculations. My guess is that it would not be (and if there is an efficiency gain, it might be offset by the added complexity), but it would be interesting to try, if for no other reason than ideological purity (if you're going to use a stochastic method, might as well make it as stochastic as possible!)

Other interesting questions arise. The locations of the all-important wavefunction nodes will now be fuzzy. What consequences does this have for a fixed-node algorithm?

Inverse matrices also appear in Sorella's Stochastic Reconfiguration method for optimization. Another use?

On a side note, I tried looking for background on Google, but searching for "stochastic matrix inversion" returned results relevant to inverting a stochastic matrix rather than stochastic methods for inverting a matrix.