deletions | additions       diff --git a/Computational Methods.tex b/Computational Methods.tex  index 7539530..91d4847 100644  --- a/Computational Methods.tex  +++ b/Computational Methods.tex 
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For the numerical calculations we avoid explicitly constructing the Kronecker product of \(P\) with itself and instead perform all matrix multiplications in the SPGL1 algorithm directly in terms of \(P\). This latter approach has much smaller memory requirements and numerical costs, ensuring that the compressed sensing process itself is rapid and not a bottleneck in our procedure. The condition \(PAP^T = B\) is satisfied up to a relative error of \(10^{-7}\) in the Frobenius norm (vectorial 2-norm).  In order to perform the undersampling required for our compressed sensing calculations, first the complete Hessians were calculated, then they were converted to the measurement basis basis,  and finally they were randomly sampled by colums. column.  Quantum mechanical Hessian Hessians  were obtained performed with the QChem 4.2~\cite{Shao_2014} software package, using density functional theory with the B3LYP exchange-correlation functional~\cite{Becke_1993} and the 6-31G* basis set. Molecular mechanics Hessian calculations Hessians  were calculated using the the MM3 force field~\cite{Allinger_1989} and the open-source package Tinker 6.2.