Zobrazeno 1 - 10
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pro vyhledávání: '"Hochstenbach, P."'
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be generalized to tr
Externí odkaz:
http://arxiv.org/abs/2406.16832
Autor:
Hochstenbach, Patrick, van Noort, Mathijs, Arndt, Dörthe, Martens, Rebekka, De Roo, Jos, Verborgh, Ruben, Bonte, Pieter, Ongenae, Femke
The Resource Description Framework (RDF) is a fundamental technology in the Semantic Web, enabling the representation and interchange of structured data. However, RDF lacks the capability to express negated statements in a generic way. As a result, e
Externí odkaz:
http://arxiv.org/abs/2406.10659
In Parts I and II of this series of papers, three new methods for the computation of eigenvalues of singular pencils were developed: rank-completing perturbations, rank-projections, and augmentation. It was observed that a straightforward structure-p
Externí odkaz:
http://arxiv.org/abs/2406.07109
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is addressed in the s
Externí odkaz:
http://arxiv.org/abs/2402.02920
A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging. Moreover, if the original data matrix possesses properties like nonneg
Externí odkaz:
http://arxiv.org/abs/2310.00636
The limited memory steepest descent method (Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex quadratic objec
Externí odkaz:
http://arxiv.org/abs/2308.15145
Logic can define how agents are provided or denied access to resources, how to interlink resources using mining processes and provide users with choices for possible next steps in a workflow. These decisions are for the most part hidden, internal to
Externí odkaz:
http://arxiv.org/abs/2305.08476
When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the gradient d
Externí odkaz:
http://arxiv.org/abs/2301.09511
Publikováno v:
Numer. Linear Algebra Appl. (2023) e2450
Standard multiparameter eigenvalue problems (MEPs) are systems of $k\ge 2$ linear $k$-parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one multivariate rectang
Externí odkaz:
http://arxiv.org/abs/2212.01867
We compare two different linear dimensionality reduction strategies for the multigroup classification problem: the trace ratio method and Fisher's discriminant analysis. Recently, trace ratio optimization has gained in popularity due to its computati
Externí odkaz:
http://arxiv.org/abs/2211.08120