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For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate…
Spectral clustering is one of the most popular graph clustering algorithms, which achieves the best performance for many scientific and engineering applications. However, existing implementations in commonly used software platforms such as…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
McDonald, Pestana and Wathen (SIAM J. Sci. Comput. 40(2), pp. A2012-A1033, 2018) present a method for preconditioning of time-dependent PDEs via approximation by a nearby time-periodic problem, that is, they employ circulant-related…
Cholesky factorization is a widely used method for solving linear systems involving symmetric, positive-definite matrices, and can be an attractive choice in applications where a high degree of numerical stability is needed. One such…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
We study parallel algorithms for the minimization of Deterministic Finite Automata (DFAs). In particular, we implement four different massively parallel algorithms on Graphics Processing Units (GPUs). Our results confirm the expectations…
We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…