相关论文: Block algorithms with augmented Rayleigh-Ritz proj…

In this article, we present a novel approach for block-structured adaptive mesh refinement (AMR) that is suitable for extreme-scale parallelism. All data structures are designed such that the size of the meta data in each distributed…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

The randomized Arnoldi process has been used in large-scale scientific computing because it produces a well-conditioned basis for the Krylov subspace more quickly than the standard Arnoldi process. However, the resulting Hessenberg matrix…

Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally…

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…

This work presents a general framework for deriving exact and approximate Newton self-consistent field (SCF) orbital optimization algorithms by leveraging concepts borrowed from differential geometry. Within this framework, we extend the…

The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms…

This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…

In this paper, we consider the convergence of a very general asynchronous-parallel algorithm called ARock, that takes many well-known asynchronous algorithms as special cases (gradient descent, proximal gradient, Douglas Rachford, ADMM,…

All-pairs compute problems apply a user-defined function to each combination of two items of a given data set. Although these problems present an abundance of parallelism, data reuse must be exploited to achieve good performance. Several…

In industrial automation, radar is a critical sensor in machine perception. However, the angular resolution of radar is inherently limited by the Rayleigh criterion, which depends on both the radar's operating wavelength and the effective…

Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that can achieve considerably stronger pruning than arc consistency. However, existing maxRRC algorithms suffer from overheads and redundancies as they…

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

We propose an incomplete algorithm for Maximum Satisfiability (MaxSAT) specifically designed to run on neural network accelerators such as GPUs and TPUs. Given a MaxSAT problem instance in conjunctive normal form, our procedure constructs a…

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…

Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…

Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…

In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex…