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03/09/2023
Optimizing network robustness via Krylov subspaces
We consider the problem of attaining either the maximal increase or redu...
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01/23/2023
On the Convergence of the Gradient Descent Method with Stochastic Fixed-point Rounding Errors under the Polyak-Lojasiewicz Inequality
When training neural networks with low-precision computation, rounding e...
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01/17/2023
A nested divide-and-conquer method for tensor Sylvester equations with positive definite hierarchically semiseparable coefficients
Linear systems with a tensor product structure arise naturally when cons...
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04/06/2022
Improved parallel-in-time integration via low-rank updates and interpolation
This work is concerned with linear matrix equations that arise from the ...
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02/24/2022
On the influence of roundoff errors on the convergence of the gradient descent method with low-precision floating-point computation
The employment of stochastic rounding schemes helps prevent stagnation o...
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07/09/2021
Divide and conquer methods for functions of matrices with banded or hierarchical low-rank structure
This work is concerned with approximating matrix functions for banded ma...
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04/23/2021
Hierarchical adaptive low-rank format with applications to discretized PDEs
A novel compressed matrix format is proposed that combines an adaptive h...
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04/01/2021
Mixed precision recursive block diagonalization for bivariate functions of matrices
Various numerical linear algebra problems can be formulated as evaluatin...
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07/09/2020
Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices
Finding the r× r submatrix of maximum volume of a matrix A∈ℝ^n× n is an ...
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02/04/2020
Compress-and-restart block Krylov subspace methods for Sylvester matrix equations
Block Krylov subspace methods (KSMs) comprise building blocks in many st...
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01/24/2020
Certified and fast computations with shallow covariance kernels
Many techniques for data science and uncertainty quantification demand e...
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09/25/2019
A computational framework for two-dimensional random walks with restarts
The treatment of two-dimensional random walks in the quarter plane leads...
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09/17/2019
hm-toolbox: Matlab software for HODLR and HSS matrices
Matrices with hierarchical low-rank structure, including HODLR and HSS m...
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08/06/2019
Rational Krylov for Stieltjes matrix functions: convergence and pole selection
Evaluating the action of a matrix function on a vector, that is x=f( M)v...
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03/06/2019
Low-rank updates and divide-and-conquer methods for quadratic matrix equations
In this work, we consider two types of large-scale quadratic matrix equa...
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02/06/2019