Mixed precision low-rank approximations and their application to block low-rank LU factorization

P Amestoy, O Boiteau, A Buttari… - IMA Journal of …, 2023 - academic.oup.com
We introduce a novel approach to exploit mixed precision arithmetic for low-rank
approximations. Our approach is based on the observation that singular vectors associated …

Combining sparse approximate factorizations with mixed-precision iterative refinement

P Amestoy, A Buttari, NJ Higham… - ACM Transactions on …, 2023 - dl.acm.org
The standard LU factorization-based solution process for linear systems can be enhanced in
speed or accuracy by employing mixed-precision iterative refinement. Most recent work has …

Parallel approximation of the maximum likelihood estimation for the prediction of large-scale geostatistics simulations

S Abdulah, H Ltaief, Y Sun, MG Genton… - … conference on cluster …, 2018 - ieeexplore.ieee.org
Maximum likelihood estimation is an important statistical technique for estimating missing
data, for example in climate and environmental applications, which are usually large and …

Step on it bringing fullwave finite-element microwave filter design up to speed

L Balewski, G Fotyga, M Mrozowski… - IEEE microwave …, 2020 - ieeexplore.ieee.org
There are many steps in the design of a microwave filter: mathematically describing the filter
characteristics, representing the circuit as a network of lumped elements or as a coupling …

HPS Cholesky: Hierarchical parallelized supernodal Cholesky with adaptive parameters

S Lin, W Yang, Y Hu, Q Cai, M Dai, H Wang… - ACM Transactions on …, 2024 - dl.acm.org
Sparse supernodal Cholesky on multi-NUMAs is challenging due to the supernode
relaxation and load balancing. In this work, we propose a novel approach to improve the …

A framework to exploit data sparsity in tile low-rank cholesky factorization

Q Cao, R Alomairy, Y Pei, G Bosilca… - 2022 IEEE …, 2022 - ieeexplore.ieee.org
We present a general framework that couples the PaRSEC runtime system and the HiCMA
numerical library to solve challenging 3D data-sparse problems. Though formally dense …

Solving block low-rank linear systems by LU factorization is numerically stable

NJ Higham, T Mary - IMA Journal of Numerical Analysis, 2022 - academic.oup.com
Block low-rank (BLR) matrices possess a blockwise low-rank property that can be exploited
to reduce the complexity of numerical linear algebra algorithms. The impact of these low …

Direct frequency-domain 3D acoustic solver with intermediate data compression benchmarked against time-domain modeling for full-waveform inversion applications

V Kostin, S Solovyev, A Bakulin… - Geophysics, 2019 - pubs.geoscienceworld.org
We have developed a fast direct solver for numerical simulation of acoustic waves in 3D
heterogeneous media. The Helmholtz equation is approximated by a 27-point finite …

A hierarchical fast direct solver for distributed memory machines with manycore nodes

C Augonnet, D Goudin, M Kuhn, X Lacoste, R Namyst… - 2019 - cea.hal.science
Compression techniques have revolutionized the Boundary Element Method used to solve
the Maxwell equations in frequency domain. In spite of the several orders of magnitude …

Sparse approximate multifrontal factorization with composite compression methods

L Claus, P Ghysels, Y Liu, TA Nhan… - ACM Transactions on …, 2023 - dl.acm.org
This article presents a fast and approximate multifrontal solver for large sparse linear
systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver …