A number of problems in probability and statistics can be addressed using the multivariate
normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a …

This article presents a fast solver for the dense “frontal” matrices that arise from the
multifrontal sparse elimination process of 3D elliptic PDEs. The solver relies on the fact that …

This article introduces a new fast direct solver for linear systems arising out of wide range of
applications, integral equations, multivariate statistics, radial basis interpolation, etc., to …

Geostatistical inverse modeling (GIM) has become a common approach to estimating
greenhouse gas fluxes at the Earth's surface using atmospheric observations. GIMs are …

We describe randomized algorithms for computing the dominant eigenmodes of the
generalized Hermitian eigenvalue problem Ax= λBx, with A Hermitian and B Hermitian and …

Abstract The Kalman Filter (KF) is a data assimilation method that has been widely used for
estimating spatially varying unknown states evolving in time. Recently, KF methods have …

We present a fast direct algorithm for computing symmetric factorizations, ie $ A= WW^ T $,
of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The …

Continuously tracking the movement of a fluid or a plume in the subsurface is a challenge
that is often encountered in applications, such as tracking a plume of injected CO2 or of a …

Reservoir monitoring aims to provide snapshots of reservoir conditions and their
uncertainties to assist operation management and risk analysis. These snapshots may …

A number of problems in probability and statistics can be addressed using the multivariate
normal (or multivariate Gaussian) distribution. In the one-dimensional case, computing the …