نتایج جستجو برای: eigenvalue gradient method

تعداد نتایج: 1735319  

Journal: :SIAM Journal on Matrix Analysis and Applications 1994

2017
Pierre Dreyfuss

We prove that under some global conditions on the maximum and the minimum eigenvalue of the matrix of the coefficients, the gradient of the (weak) solution of some degenerate elliptic equations has higher integrability than expected. Technically we adapt the Giaquinta-Modica regularity method in some degenerate cases. When the dimension is two, a consequence of our result is a new Hölder contin...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2015
A E Lindsay T Kolokolnikov J C Tzou

We consider the mean first passage time (MFPT) of a two-dimensional diffusing particle to a small trap with a distribution of absorbing and reflecting sections. High-order asymptotic formulas for the MFPT and the fundamental eigenvalue of the Laplacian are derived which extend previously obtained results and show how the orientation of the trap affects the mean time to capture. We obtain a simp...

Journal: :SIAM J. Matrix Analysis Applications 2009
Michiel E. Hochstenbach Yvan Notay

The Jacobi–Davidson method is an eigenvalue solver which uses the iterative (and in general inaccurate) solution of inner linear systems to progress, in an outer iteration, towards a particular solution of the eigenproblem. In this paper we prove a relation between the residual norm of the inner linear system and the residual norm of the eigenvalue problem. We show that the latter may be estima...

Journal: :Asia-Pacific Journal of Operational Research 2023

Using second-order optimization methods for training deep neural networks (DNNs) has attracted many researchers. A recently proposed method, Eigenvalue-corrected Kronecker Factorization (EKFAC) (George et al., 2018), proposes an interpretation of viewing natural gradient update as a diagonal and corrects the inaccurate re-scaling factor in Kronecker-factored eigenbasis. Gao al. (2020) considers...

1998
Frank Wijnands Thomas Rasmussen Hugo J. W. M. Hoekstra Jørn H. Povlsen René M. de Ridder

A method, based on a semivectorial finite difference scheme, is described to construct modal fields for any twodimensional refractive-index profile which is constant except at abrupt interfaces. The modal fields correspond to eigenvectors of the matrix equation to be solved. In order to find the eigenvectors and their corresponding eigenvalues, the matrix equation is formulated according to the...

A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

Journal: :journal of linear and topological algebra (jlta) 0
m amirfakhrian department of mathematics, islamic azad university, central tehran branch, po. code 14168-94351, iran. f mohammad department of mathematics, islamic azad university, central tehran branch, po. code 14168-94351, iran.

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

Journal: :SIAM Journal on Optimization 2008
Alexandre d'Aspremont

We show that the optimal complexity of Nesterov’s smooth first-order optimization algorithm is preserved when the gradient is only computed up to a small, uniformly bounded error. In applications of this method to semidefinite programs, this often means computing only a few dominant eigenvalues of the current iterate instead of a full matrix exponential, which significantly reduces the method’s...

Journal: :SIAM J. Matrix Analysis Applications 2015
Ruey-Lin Chern Han-En Hsieh Tsung-Ming Huang Wen-Wei Lin Weichung Wang

This article focuses on solving the generalized eigenvalue problems (GEP) arising in the source-free Maxwell equation with magnetoelectric coupling effects that models three-dimensional complex media. The goal is to compute the smallest positive eigenvalues, and the main challenge is that the coefficient matrix in the discrete Maxwell equation is indefinite and degenerate. To overcome this diff...

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