Zobrazeno 1 - 10
of 66
pro vyhledávání: '"KNYAZEV, ANDREW V."'
Convergence rates of block iterations for solving eigenvalue problems typically measure errors of Ritz values approximating eigenvalues. The errors of the Ritz values are commonly bounded in terms of principal angles between the initial or iterative
Externí odkaz:
http://arxiv.org/abs/2211.01499
Autor:
Knyazev, Andrew V.
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed
Externí odkaz:
http://arxiv.org/abs/1701.01394
Publikováno v:
2016 American Control Conference (ACC), Boston, MA, 2016, pp. 5605-5611
Exploiting sparsity in Semidefinite Programs (SDP) is critical to solving large-scale problems. The chordal completion based maximal clique decomposition is the preferred approach for exploiting sparsity in SDPs. In this paper, we show that the maxim
Externí odkaz:
http://arxiv.org/abs/1509.08021
Autor:
Argentati, Merico E., Knyazev, Andrew V., Neymeyr, Klaus, Ovtchinnikov, Evgueni E., Zhou, Ming
Publikováno v:
Foundations of Computational Mathematics, 17(3), pp. 1-15, 2017. Online: 23 November 2015
Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using multilevel pr
Externí odkaz:
http://arxiv.org/abs/1412.5005
Publikováno v:
Procedia Computer Science, v. 51, pp. 276-285, 2015
We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid when used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (S
Externí odkaz:
http://arxiv.org/abs/1212.6680
Autor:
Zhu, Peizhen, Knyazev, Andrew V.
Publikováno v:
Journal of Numerical Mathematics. 2013, 21(4) 325-340
Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS ar
Externí odkaz:
http://arxiv.org/abs/1209.0523
Publikováno v:
SIAM Journal on Matrix Analysis and Applications 2013 34:1, 244-256
The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If $x$ is an eigenvector of a self-adjoint bounded operator $A$ in a Hilbert space, then the RQ of the vecto
Externí odkaz:
http://arxiv.org/abs/1207.3240
Publikováno v:
SIAM Journal on Scientific Computing 2013 35:2, A696-A718
We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the prec
Externí odkaz:
http://arxiv.org/abs/1104.4530
Autor:
Knyazev, Andrew V., Neymeyr, Klaus
Publikováno v:
SIAM. J. Matrix Anal. & Appl. Volume 31, Issue 2, pp. 621-628 (2009)
Preconditioned eigenvalue solvers (eigensolvers) are gaining popularity, but their convergence theory remains sparse and complex. We consider the simplest preconditioned eigensolver--the gradient iterative method with a fixed step size--for symmetric
Externí odkaz:
http://arxiv.org/abs/0801.3099
Autor:
Knyazev, Andrew V.
Publikováno v:
Comput. Methods Appl. Mech.Engrg. 196, Issues 37-40, 3742-3749 (2007)
We investigate degenerate saddle point problems, which can be viewed as limit cases of standard mixed formulations of symmetric problems with large jumps in coefficients. We prove that they are well-posed in a standard norm despite the degeneracy. By
Externí odkaz:
http://arxiv.org/abs/0704.1066