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08/30/2023
A spectrum adaptive kernel polynomial method
The kernel polynomial method (KPM) is a powerful numerical method for ap...
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06/29/2023
Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm
Given an n by n matrix A and an n-vector b, along with a rational functi...
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03/06/2023
Near-Optimality Guarantees for Approximating Rational Matrix Functions by the Lanczos Method
We study the Lanczos method for approximating the action of a symmetric ...
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03/03/2023
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
We study the GMRES algorithm applied to linear systems of equations invo...
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02/28/2023
Stability of the Lanczos algorithm on matrices with regular spectral distributions
We study the stability of the Lanczos algorithm run on problems whose ei...
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11/28/2022
A posteriori error bounds for the block-Lanczos method for matrix function approximation
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (20...
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06/15/2022
On the fast convergence of minibatch heavy ball momentum
Simple stochastic momentum methods are widely used in machine learning o...
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05/03/2022
Krylov-aware stochastic trace estimation
We introduce an algorithm for estimating the trace of a matrix function ...
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04/18/2022
Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
We describe a numerical algorithm for approximating the equilibrium-redu...
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04/05/2022
Randomized matrix-free quadrature for spectrum and spectral sum approximation
We study randomized matrix-free quadrature algorithms for spectrum and s...
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02/23/2022
Low-memory Krylov subspace methods for optimal rational matrix function approximation
We describe a Lanczos-based algorithm for approximating the product of a...
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06/17/2021
Error bounds for Lanczos-based matrix function approximation
We analyze the Lanczos method for matrix function approximation (Lanczos...
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05/13/2021
Analysis of stochastic Lanczos quadrature for spectrum approximation
The cumulative empirical spectral measure (CESM) Φ[𝐀] : ℝ→ [0,1] of a n×...
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07/21/2020
Rounding random variables to finite precision
In this paper, we provide general bounds on the mean absolute difference...
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05/14/2019
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic
We consider three mathematically equivalent variants of the conjugate gr...
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05/04/2019
Predict-and-recompute conjugate gradient variants
The standard implementation of the conjugate gradient algorithm suffers ...
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05/04/2019