# Updating the inverse of a matrix hager

One advantage of En KFs is that advancing the pdf in time is achieved by simply advancing each member of the ensemble.

For a survey of En KF and related data assimilation techniques, see G.

So, take a stroll down memory lane to remember all of our past Word of the Year selections.

The ensemble Kalman filter (En KF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models.

Since the ensemble covariance is rank deficient (there are many more state variables, typically millions, than the ensemble members, typically less than a hundred), it has large terms for pairs of points that are spatially distant.

A parallelizable direct solution of integral equation methods is proposed for electromagnetic scattering analysis in low to intermediate frequency regime.

There are mainly two parts of the proposed direct solution: forward decomposition and backward substitution.

Furthermore, an effective preconditioner with a reasonable selection criterion of the diagonal blocks region is proposed to accelerate the convergence of the iterative solver.

The proposed solution is independent of the Green's function, and it is suitable for all the integral equation methods.

For the forward decomposition, the dense impedance matrix is decomposed of the product of several block diagonal matrices implicitly, which is shown to be ) complexity as well.