Related papers: An Efficient Parallel Solver for SDD Linear System…
Sorting has been one of the most challenging studied problems in different scientific researches. Although many techniques and algorithms have been proposed on the theory of having efficient parallel sorting implementation, however…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…
We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…
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 these matrices can be efficiently represented as a…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…
A fast direct inversion scheme for the large sparse systems of linear equations resulting from the discretization of elliptic partial differential equations in two dimensions is given. The scheme is described for the particular case of a…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
A symmetric matrix is called a Laplacian if it has nonpositive off-diagonal entries and zero row sums. Since the seminal work of Spielman and Teng (2004) on solving Laplacian linear systems in nearly linear time, several algorithms have…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
We present a new parallel algorithm for solving triangular systems with multiple right hand sides (TRSM). TRSM is used extensively in numerical linear algebra computations, both to solve triangular linear systems of equations as well as to…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
With the rapid growth of unstructured and semistructured data, parallelizing graph algorithms has become essential for efficiency. However, due to the inherent irregularity in computation, memory access patterns, and communication, graph…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…