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Generalized Rybicki Press algorithm
Sivaram Ambikasaran
This article discusses a more general and numerically stable Rybicki Press algorithm, which enables inverting and computing determinants of covariance matrices, whose elements are…
The Inverse Fast Multipole Method
Sivaram Ambikasaran, Eric Darve
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolati…
Fast symmetric factorization of hierarchical matrices with applications
Sivaram Ambikasaran, Michael O'Neil, Karan Raj Singh
We present a fast direct algorithm for computing symmetric factorizations, i.e. , of symmetric positive-definite hierarchical matrices with weak-admissibility conditions.…
A Kalman filter powered by -matrices for quasi-continuous data assimilation problems
Judith Y. Li, Sivaram Ambikasaran, Eric F. Darve +1
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 CO or…
A fast direct solver for high frequency scattering from a large cavity in two dimensions
Jun Lai, Sivaram Ambikasaran, Leslie F. Greengard
We present a fast direct solver for the simulation of electromagnetic scattering from an arbitrarily-shaped, large, empty cavity embedded in an infinite perfectly conducting half s…
Fast Direct Methods for Gaussian Processes
Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard +2
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 fo…
A Fast Block Low-Rank Dense Solver with Applications to Finite-Element Matrices
Amirhossein Aminfar, Sivaram Ambikasaran, Eric Darve
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…