1 citations · 1 across the 12 of their papers we have counts for
14 papers
Incremental Column Subset Selection via Conditional Determinantal Point Processes
Laura Grigori, Zhipeng Xue
Column subset selection aims to seek a small set of representative columns that accurately approximates a given matrix. We study this problem from the perspective of determinantal…
Randomized Block Davidson Eigensolvers for Plane-Wave Density-Functional Theory
Moritz Gubler, Taejun Park, Augustin Bussy +4
Iterative diagonalization is the dominant cost of plane-wave density-functional theory (DFT), with search-space orthogonalization scaling particularly quickly with problem size and…
Accelerating the Canonical Polyadic Alternating Least Squares Optimization via a Randomized Interpolative Decomposition
Israa Fakih, Laura Grigori, Karl Pierce
We present a novel leverage score-based sampling strategy for the randomized alternating least squares optimization (ALS) of the canonical polyadic decomposition (CPD-ALS). Unlike…
Sketch low-rank dynamics: orthogonal vs. oblique projections
Benjamin Carrel, Laura Grigori
We study how sketching techniques from randomized numerical linear algebra can be incorporated into the dynamical low-rank approximation (DLRA) of large-scale matrix differential e…
Attention Mechanisms Through the Lens of Numerical Methods: Approximation Methods and Alternative Formulations
Michel Fabrice Serret, Alice Cortinovis, Yijun Dong +10
The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale i…
Communication Lower Bounds and Algorithms for Sketching with Random Dense Matrices
Hussam Al Daas, Grey Ballard, Laura Grigori +4
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in…
Restoring similarity in randomized Krylov methods with applications to eigenvalue problems and matrix functions
Laura Grigori, Daniel Kressner, Nian Shao +1
The randomized Arnoldi process has been used in large-scale scientific computing because it produces a well-conditioned basis for the Krylov subspace more quickly than the standard…
Randomized orthogonalization and Krylov subspace methods: principles and algorithms
Jean-Guillaume de Damas, Laura Grigori, Igor Simunec +1
We present an overview of randomized orthogonalization techniques that construct a well-conditioned basis whose sketch is orthonormal. Randomized orthogonalization has recently eme…
Randomized biorthogonalization through a two-sided Gram-Schmidt process
Laura Grigori, Lorenzo Piccinini, Igor Simunec
We propose and analyze a randomized two-sided Gram-Schmidt process for the biorthogonalization of two given matrices . The algorithm aims to find tw…
Efficient QR-based Column Subset Selection through Randomized Sparse Embeddings
Israa Fakih, Laura Grigori
In this paper, we introduce an efficient algorithm for column subset selection that combines the column-pivoted QR factorization with sparse subspace embeddings. The proposed metho…
Randomized Krylov-Schur eigensolver with deflation
Jean-Guillaume de Damas, Laura Grigori
This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple i…
Randomized strong rank-revealing QR for column subset selection and low-rank matrix approximation
Laura Grigori, Zhipeng Xue
We discuss a randomized strong rank-revealing QR factorization that effectively reveals the spectrum of a matrix . This factorization can be used to address problems su…
Randomized Implicitly Restarted Arnoldi method for the non-symmetric eigenvalue problem
Jean-Guillaume de Damas, Laura Grigori
In this paper, we introduce a randomized algorithm for solving the non-symmetric eigenvalue problem, referred to as randomized Implicitly Restarted Arnoldi (rIRA). This method reli…
Factorized structure of the long-range two-electron integrals tensor and its application in quantum chemistry
Siwar Badreddine, Igor Chollet, Laura Grigori
We introduce two new approximation methods for the numerical evaluation of the long-range Coulomb potential and the approximation of the resulting high dimensional Two-Electron Int…