1k citations · 1.2k across the 20 of their papers we have counts for
23 papers
LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability
Sumit Singh, Shrirup Dutta, Sivaram Ambikasaran
We propose Local Chebyshev Cross-Approximation (LoCCA), a data-driven framework that bridges smooth polynomial interpolation with flexible matrix factorizations. LoCCA dynamically…
Continuous Cross Approximation of Matrices Arising Out of Kernel Functions
Sumit Singh, Sivaram Ambikasaran
We propose a residual energy-based framework for constructing low-rank approximations of kernel matrices arising from continuous kernel functions. The method operates in a continuo…
Rank of Matrices Arising out of Singular Kernel Functions
Sumit Singh, Sivaram Ambikasaran
Kernel functions are frequently encountered in differential equations and machine learning applications. In this work, we study the rank of matrices arising out of the kernel funct…
A hybrid interpolation ACA accelerated method for parabolic boundary integral operators
Sivaram Ambikasaran, Ritesh Khan, Johannes Tausch +1
We consider piecewise polynomial discontinuous Galerkin discretizations of boundary integral reformulations of the heat equation. The resulting linear systems are dense and block-l…
New Algebraic Fast Algorithms for -body Problems in Two and Three Dimensions
Ritesh Khan, Sivaram Ambikasaran
We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product (MVP) for -body problems in dimensions, namely efficient $\mathc…
HODLR3D: Hierarchical matrices for -body problems in three dimensions
V A Kandappan, Vaishnavi Gujjula, Sivaram Ambikasaran
This article introduces HODLR3D, a class of hierarchical matrices arising out of -body problems in three dimensions. HODLR3D relies on the fact that certain off-diagonal matrix…
Algebraic Inverse Fast Multipole Method: A fast direct solver that is better than HODLR based fast direct solver
Vaishnavi Gujjula, Sivaram Ambikasaran
This article presents a fast direct solver, termed Algebraic Inverse Fast Multipole Method (from now on abbreviated as AIFMM), for linear systems arising out of -body problems.…
HODLRD: A new Black-box fast algorithm for -body problems in -dimensions with guaranteed error bounds
Ritesh Khan, V A Kandappan, Sivaram Ambikasaran
In this article, we prove new theorems bounding the rank of different sub-matrices arising from these kernel functions. Bounds like these are often useful for analyzing the complex…
Spectrum of MATLABs magic squares
Hariprasad Manjunath, Sivaram Ambikasaran
This article looks at the eigenvalues of magic squares generated by the MATLAB's magic() function. The magic() function constructs doubly even () magic squares, singl…
HODLR2D: A new class of Hierarchical matrices
V A Kandappan, Vaishnavi Gujjula, Sivaram Ambikasaran
This article introduces HODLR2D, a new hierarchical low-rank representation for a class of dense matrices arising out of body problems in two dimensions. Using this new hierarc…
A new Directional Algebraic Fast Multipole Method based iterative solver for the Lippmann-Schwinger equation accelerated with HODLR preconditioner
Vaishnavi Gujjula, Sivaram Ambikasaran
We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume pote…
A new Nested Cross Approximation
Vaishnavi Gujjula, Sivaram Ambikasaran
In this article, we present a new Nested Cross Approximation (NNCA) for constructing H2 matrices. It differs from the existing NCAs~\cite{bebendorf2012constructing, zhao2019fast} i…
Fast and scalable Gaussian process modeling with applications to astronomical time series
Daniel Foreman-Mackey, Eric Agol, Sivaram Ambikasaran +1
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Proce…
An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities
Sivaram Ambikasaran, Krithika Narayanaswamy
Using accurate multi-component diffusion treatment in numerical combustion studies remains formidable due to the computational cost associated with solving for diffusion velocities…
Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimension
Sivaram Ambikasaran, Carlos Borges, Lise-Marie Imbert-Gerard +1
We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered fie…
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…
A simple way to speedup Gauss Elimination
Sivaram Ambikasaran
This article looks at a simple modification to speedup the conventional Gauss Elimination. The proposed modification speeds up the conventional Gauss Elimination by a factor of nea…