Search · four archives
Search · four archives
9 papers · ranked by Valyu relevance
Haoze He, Daniel Kreßner
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing this task. RJD applies a standard eigenvalue solver to random…
Bowen Li, Jianfeng Lu, Ziang Yu
This work aims to numerically construct exactly commuting matrices close to given almost commuting ones, which is equivalent to the joint approximate diagonalization problem. We first prove that almost commuting matrices generically have approximate common eigenvectors that are almost orthogonal to each other. Based on…
Abd‐Krim Seghouane, Yousef Saad
Given a set of p symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these p matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural…
Haoze He, Daniel Kressner, Bor Plestenjak
It is well known that a family of ${n}\times{n}$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to…
Maximilian Ramgraber, Daniel Sharp, Mathieu Le Provost, Youssef Marzouk
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box models, however, these representations are rarely known. We discuss how to…
Manuel Schürch, Dario Azzimonti, Alessio Benavoli, Marco Zaffalon
Gaussian processes (GPs) are an important tool in machine learning and statistics. However, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past…
Johanna Gehlen, Jie Li, Cillian Hourican, Stavroula Tassi + 7 more
'Pashupati P. Mishra' 'Terho Lehtimäki' 'Mika Kähönen' 'Olli Raitakari' 'Jos A. Bosch' 'Rick Quax' 'Chaoming Song'] Higher-order relationships are a central concept in the science of complex systems. A popular method of attempting to estimate the higher-order relationships of synergy and redundancy from data is through…
Takuya Okuyama, André Röhm, Takatomo Mihana, Makoto Naruse + 1 more
Matrix multiplication is important in various information-processing applications, including the computation of eigenvalues and eigenvectors, and in combinatorial optimization algorithms. Therefore, reducing the computation time of matrix products is essential to speed up scientific and practical calculations. Several…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…