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Beyond Expectation: Concentration Inequalities for Randomized Iterative Methods
Toby Anderson, Max Collins, Jamie Haddock +2
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprin…
Scientific Applications Leveraging Randomized Linear Algebra
Vivak Patel, D. Adrian Maldonado, Maksim Melnichenko +5
This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications…
Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations
Jackie Lok, Elizaveta Rebrova
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the sol…
Data-Driven, ML-assisted Approaches to Problem Well-Posedness
Tom Bertalan, George A. Kevrekidis, Eleni D Koronaki +3
Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. We…
On Trimming Tensor-structured Measurements and Efficient Low-rank Tensor Recovery
Shambhavi Suryanarayanan, Elizaveta Rebrova
In this paper, we take a step towards developing efficient hard thresholding methods for low-rank tensor recovery from memory-efficient linear measurements with tensorial structure…
Randomized Kaczmarz Methods with Beyond-Krylov Convergence
Michał Dereziński, Deanna Needell, Elizaveta Rebrova +1
Randomized Kaczmarz methods form a family of linear system solvers which converge by repeatedly projecting their iterates onto randomly sampled equations. While effective in some c…