simpeg.directives.PairedBetaEstimate_ByEig.initialize#

PairedBetaEstimate_ByEig.initialize()[source]#

The initial beta is calculated by comparing the estimated eigenvalues of JTJ and WTW. To estimate the eigenvector of A, we will use one iteration of the Power Method:

x1=Ax0

Given this (very course) approximation of the eigenvector, we can use the Rayleigh quotient to approximate the largest eigenvalue.

λ0=xAxxx

We will approximate the largest eigenvalue for both JtJ and WtW, and use some ratio of the quotient to estimate beta0.

β0=γxJJxxWWx
Return type:

float

Returns:

beta0