Randomized numerical linear algebra: A perspective on the field with an eye to software
Randomized numerical linear algebra-RandNLA, for short-concerns the use of
randomization as a resource to develop improved algorithms for large-scale linear algebra …
randomization as a resource to develop improved algorithms for large-scale linear algebra …
Randomized block Gram-Schmidt process for solution of linear systems and eigenvalue problems
O Balabanov, L Grigori - arXiv preprint arXiv:2111.14641, 2021 - arxiv.org
This article introduces randomized block Gram-Schmidt process (RBGS) for QR
decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm …
decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm …
An improved Shifted CholeskyQR based on columns
Shifted CholeskyQR3 is designed to address the QR factorization of ill-conditioned matrices.
This algorithm introduces a shift parameter $ s $ to prevent failure during the initial Cholesky …
This algorithm introduces a shift parameter $ s $ to prevent failure during the initial Cholesky …
CholeskyQR for sparse matrices
H Guan, Y Fan - arXiv preprint arXiv:2410.06525, 2024 - arxiv.org
CholeskyQR is an efficient algorithm for QR factorization with several advantages compared
with orhter algorithms. In order to improve its orthogonality, CholeskyQR2 is developed\cite …
with orhter algorithms. In order to improve its orthogonality, CholeskyQR2 is developed\cite …
Randomized orthogonal projection methods for Krylov subspace solvers
E Timsit, L Grigori, O Balabanov - arXiv preprint arXiv:2302.07466, 2023 - arxiv.org
Randomized orthogonal projection methods (ROPMs) can be used to speed up the
computation of Krylov subspace methods in various contexts. Through a theoretical and …
computation of Krylov subspace methods in various contexts. Through a theoretical and …
Analysis of Randomized Householder-Cholesky QR Factorization with Multisketching
CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-
and-skinny QR factorizations since they attain high performance on current computer …
and-skinny QR factorizations since they attain high performance on current computer …
Probabilistic error analysis of CholeskyQR based on columns
H Guan, Y Fan - arXiv preprint arXiv:2410.09389, 2024 - arxiv.org
CholeskyQR-type algorithms are very popular in both academia and industry in recent
years. It could make a balance between the computational cost, accuracy and speed …
years. It could make a balance between the computational cost, accuracy and speed …
A Cholesky QR type algorithm for computing tall-skinny QR factorization with column pivoting
T Fukaya, Y Nakatsukasa… - 2024 IEEE International …, 2024 - ieeexplore.ieee.org
We consider computing the QR factorization with column pivoting (QRCP) for a tall and
skinny matrix, which has important applications including low-rank approximation and rank …
skinny matrix, which has important applications including low-rank approximation and rank …
Deterministic and randomized LU-Householder CholeskyQR
H Guan, Y Fan - arXiv preprint arXiv:2412.06551, 2024 - arxiv.org
In this work, we focus on improving LU-CholeskyQR2\cite {LUChol}. Compared to other
deterministic and randomized CholeskyQR-type algorithms, it does not require a sufficient …
deterministic and randomized CholeskyQR-type algorithms, it does not require a sufficient …
Two-Stage Block Orthogonalization to Improve Performance of -step GMRES
On current computer architectures, GMRES'performance can be limited by its
communication cost to generate orthonormal basis vectors of the Krylov subspace. To …
communication cost to generate orthonormal basis vectors of the Krylov subspace. To …