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We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
We introduce RandRAND, a new class of randomized preconditioning methods for large-scale linear systems. RandRAND deflates the spectrum via efficient orthogonal projections onto random subspaces, without computing eigenpairs or low-rank…
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…
In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…
We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of…
Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…
The performance of short polar codes under successive cancellation (SC) and SC list (SCL) decoding is analyzed for the case where the decoder messages are coarsely quantized. This setting is of particular interest for applications requiring…
QR bar codes are prototypical images for which part of the image is a priori known (required patterns). Open source bar code readers, such as ZBar, are readily available. We exploit both these facts to provide and assess purely…
Hybridizable discretizations allow for the elimination of local degrees-of-freedom leading to reduced linear systems. In this paper, we determine and analyse an approach to construct parameter-robust preconditioners for these reduced…
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…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of…
There is growing awareness that errors in the model equations cannot be ignored in data assimilation methods such as four-dimensional variational assimilation (4D-Var). If allowed for, more information can be extracted from observations,…
We describe a randomized variant of the block conjugate gradient method for solving a single positive-definite linear system of equations. Our method provably outperforms preconditioned conjugate gradient with a broad-class of…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
Quantum computing has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A $n$-qubit quantum system is capable of providing $2^{n}$ computational space…
This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that…
Neural image compression has been shown to outperform traditional image codecs in terms of rate-distortion performance. However, quantization introduces errors in the compression process, which can degrade the quality of the compressed…
We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…