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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…
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…