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Stochastic trace estimation for positive trace-class operators
Zvonimir Bujanović, Luka Grubišić, Daniel Kressner +1
Implicit trace estimation aims to approximate the trace of a matrix or linear operator accessible only through matrix-vector or operator-vector products. In the matrix setting, the…
Stochastic trace estimation with tensor train random vectors
Zvonimir Bujanović, Daniel Kressner, Hrvoje Olić
Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products. However, in tensor-structured sett…
Kernel-based linear system identification using augmented Krylov subspaces
Fabio Matti, Martin Skovgaard Andersen, Tianshi Chen +1
We propose a novel Krylov subspace method for estimating the finite impulse response (FIR) of a one-dimensional linear time-invariant systems. The method approximates the system's…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
A novel Krylov subspace method for approximating Fréchet derivatives of large-scale matrix functions
Daniel Kressner, Peter Oehme
We present a novel Krylov subspace method for approximating $L_f(A, E) \vc{b}$, the matrix-vector product of the Fréchet derivative of a large-scale matrix function $f(…
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…