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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…
In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the…
We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block updates in the solution, and a dynamic proposal distribution…
We present a novel linear solver that works well for large systems obtained from discretizing PDEs. It is robust and, for the examples we studied, the computational effort scales linearly with the number of equations. The algorithm is based…
This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
Solving large, sparse linear systems is a fundamental workload in scientific computing and engineering simulations, often dominating runtime and energy consumption in high-performance computing (HPC) applications. In this work, we explore…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…
Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well…
Tremendous variation in the scale of people/head size is a critical problem for crowd counting. To improve the scale invariance of feature representation, recent works extensively employ Convolutional Neural Networks with multi-column…
We introduce Flower, a solver for linear inverse problems. It leverages a pre-trained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps:…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
In this paper, we show the effectiveness of a pipeline implementation of Dynamic Programming (DP) on GPU. As an example, we explain how to solve a matrix-chain multiplication (MCM) problem by DP on GPU. This problem can be sequentially…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…