Related papers: Efficient Computation of Sparse Matrix Functions f…

The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…

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…

Chebyshev expansion coefficients can be computed efficiently by using the FFT, and for smooth functions the resulting approximation is close to optimal, with computations that are numerically stable. Given sufficiently accurate function…

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…

Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points.…

We develop the gapped-filtering method, whereby a short Chebyshev expansion accurately represents the density-matrix operator. The method optimizes the Chebyshev coefficients to give the correct density matrix at all energies except within…

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations.…

Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems.…

Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse…

This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner…

We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new…

We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence…

Deep learning demonstrates effectiveness across a wide range of tasks. However, the dense and over-parameterized nature of these models results in significant resource consumption during deployment. In response to this issue, weight…

Deep Learning (DL) has achieved unprecedented success in various application domains. Meanwhile, model pruning has emerged as a viable solution to reduce the footprint of DL models in mobile applications, without compromising their…

Matrix factorization (MF) can extract the low-rank features and integrate the information of the data manifold distribution from high-dimensional data, which can consider the nonlinear neighbourhood information. Thus, MF has drawn wide…

The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…

We propose a method for strict error control in sparse approximate matrix-matrix multiplication. The method combines an error bound and a parameter sweep to select an appropriate threshold value. The scheme for error control and the sparse…

Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of…

To address the challenge of performance portability, and facilitate the implementation of electronic structure solvers, we developed the Basic Matrix Library (BML) and Parallel, Rapid O(N) and Graph-based Recursive Electronic Structure…