Related papers: Efficient Computation of Sparse Matrix Functions f…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
We present a computationally efficient approach to perform large-scale all-electron density functional theory calculations by enriching the classical finite element basis with compactly supported atom-centered numerical basis functions that…
We present sparse interpolation algorithms for recovering a polynomial with $\le B$ terms from $N$ evaluations at distinct values for the variable when $\le E$ of the evaluations can be erroneous. Our algorithms perform exact arithmetic in…
As the size of Deep Neural Networks (DNNs) increases dramatically to achieve high accuracy, the DNNs require a large amount of computations and memory footprint. Pruning, which produces a sparse neural network, is one of the solutions to…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Sparse linear system solvers ($Ax=b$) are critical computational kernels in Electronic Design Automation (EDA), underpinning vital simulations for modern IC and system design. Applications like power integrity verification and…
We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…
An algorithm is provided for performing polynomial feature expansions that both operates on and produces compressed sparse row (CSR) matrices. Previously, no such algorithm existed, and performing polynomial expansions on CSR matrices…
Most, if not all the modern scientific simulation packages utilize matrix algebra operations. Among the operation of the linear algebra, one of the most important kernels is the multiplication of matrices, dense and sparse. Examples of…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
As modern massively parallel clusters are getting larger with beefier compute nodes, traditional parallel eigensolvers, such as direct solvers, struggle keeping the pace with the hardware evolution and being able to scale efficiently due to…
We present an implementation of Pagh's compressed matrix multiplication algorithm, a randomized algorithm that constructs sketches of matrices to compute an unbiased estimate of their product. By leveraging fast polynomial multiplication…
Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis and…
Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current…
In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V-cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind. For our test…