Zobrazeno 1 - 10
of 163
pro vyhledávání: '"HOCHSTENBACH, MICHIEL E."'
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
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 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
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
We present block variants of the discrete empirical interpolation method (DEIM); as a particular application, we will consider a CUR factorization. The block DEIM algorithms are based on the concept of the maximum volume of submatrices and a rank-rev
Externí odkaz:
http://arxiv.org/abs/2208.02213
Publikováno v:
SIAM Journal on Matrix Analysis and Applications 44 (2023) 1589-1618
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two alternative methods
Externí odkaz:
http://arxiv.org/abs/2208.01359
Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh quotient, and an
Externí odkaz:
http://arxiv.org/abs/2206.13457