Related papers: Assessment of localized and randomized algorithms …
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
This paper highlights new opportunities for designing large-scale machine learning systems as a consequence of blurring traditional boundaries that have allowed algorithm designers and application-level practitioners to stay -- for the most…
Factorizing large matrices by QR with column pivoting (QRCP) is substantially more expensive than QR without pivoting, owing to communication costs required for pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the…
This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of…
Researchers have long touted a vision of the future enabled by a proliferation of internet-of-things devices, including smart sensors, homes, and cities. Increasingly, embedding intelligence in such devices involves the use of deep neural…
Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case).…
With the rapid development of large language models (LLMs) and the growing demand for personalized content, recommendation systems have become critical in enhancing user experience and driving engagement. Collaborative filtering algorithms,…
Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip…