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Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the quality o
Externí odkaz:
http://arxiv.org/abs/2410.16455
This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions. We propose a stochastic method
Externí odkaz:
http://arxiv.org/abs/2410.08297
Autor:
Yang, Yanfei
The hybrid LSMR algorithm is proposed for large-scale general-form regularization. It is based on a Krylov subspace projection method where the matrix $A$ is first projected onto a subspace, typically a Krylov subspace, which is implemented via the G
Externí odkaz:
http://arxiv.org/abs/2409.09104
Autor:
Chu, Ya-Chi, Cortinovis, Alice
In this work, we analyze the variance of a stochastic estimator for computing Schatten norms of matrices. The estimator extracts information from a single sketch of the matrix, that is, the product of the matrix with a few standard Gaussian random ve
Externí odkaz:
http://arxiv.org/abs/2408.17414
Autor:
Chu, Delin, Mehrmann, Volker
The relationship between port-Hamiltonian and positive real descriptor systems is investigated. It is well-known that port-Hamiltonian systems are positive real, but the converse implication does not always hold. In [K. Cherifi, H. Gernandt, and D. H
Externí odkaz:
http://arxiv.org/abs/2408.14115
Autor:
Graf, Emil, Townsend, Alex
We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are constructed at intermediate steps. In particular, we give multidimensiona
Externí odkaz:
http://arxiv.org/abs/2408.02805
Autor:
Garrison, James E., Ipsen, Ilse C. F.
We a present and analyze rpCholesky-QR, a randomized preconditioned Cholesky-QR algorithm for computing the thin QR factorization of real mxn matrices with rank n. rpCholesky-QR has a low orthogonalization error, a residual on the order of machine pr
Externí odkaz:
http://arxiv.org/abs/2406.11751
Autor:
Chu, Delin, Mehrmann, Volker
While port-Hamiltonian descriptor systems are known to be stable and passive, they may not be asymptotically stable or strictly passive. Necessary and sufficient conditions are presented when these properties as well as the regularity and the index o
Externí odkaz:
http://arxiv.org/abs/2406.08994
Autor:
Bist, Avisek, Behera, Namita
Consider a multivariable state space system and associated transfer function G({\lambda}). The aim of this paper is to define and analyze two vector spaces of matrix pencils associated with the matrix G({\lambda}) and show that almost all of these pe
Externí odkaz:
http://arxiv.org/abs/2405.15819
Autor:
Chang, Chao, Yang, Yuning
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders. To address
Externí odkaz:
http://arxiv.org/abs/2404.14783