32 citations · 50 across the 10 of their papers we have counts for
11 papers · 1 filter
Stable Matrix-Free Q-less QR via Preconditioning and Randomization
Oleg Balabanov, Maksim Melnichenko, Michael W. Mahoney
This article develops matrix-free Q-less QR algorithms for orthogonalizing tall linear operators. Our main algorithm, CQRRTO, uses randomized preconditioning to make a single Chole…
Preconditioning via Randomized Range Deflation (RandRAND)
Oleg Balabanov, Caleb Ju, Kaiwen He +2
We introduce RandRAND, a new class of randomized preconditioning methods for large-scale linear systems. RandRAND deflates the spectrum via efficient orthogonal projections onto ra…
CholeskyQR with Randomization and Pivoting for Tall Matrices (CQRRPT)
Maksim Melnichenko, Oleg Balabanov, Riley Murray +3
This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully…
Randomized Orthogonal Projection Methods for Krylov Subspace Solvers
Edouard Timsit, Laura Grigori, Oleg Balabanov
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investi…
Randomized Cholesky QR factorizations
Oleg Balabanov
This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix . Instead of computing the R factor from , as is done by stand…
Block subsampled randomized Hadamard transform for low-rank approximation on distributed architectures
Oleg Balabanov, Matthias Beaupere, Laura Grigori +1
This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-kn…
Randomized block Gram-Schmidt process for solution of linear systems and eigenvalue problems
Oleg Balabanov, Laura Grigori
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its k…
Random sketching of operators with application to learning preconditioners
Oleg Balabanov, Anthony Nouy, Alexandre Pasco
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a lo…
Randomized Gram-Schmidt process with application to GMRES
Oleg Balabanov, Laura Grigori
A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive…
Randomized linear algebra for model reduction. Part II: minimal residual methods and dictionary-based approximation
Oleg Balabanov, Anthony Nouy
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy…
Randomized linear algebra for model reduction. Part I: Galerkin methods and error estimation
Oleg Balabanov, Anthony Nouy
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is…