Zobrazeno 1 - 10
of 2 099
pro vyhledávání: '"Ritz values"'
Autor:
Zhou, Ming, Neymeyr, Klaus
Many popular eigensolvers for large and sparse Hermitian matrices or matrix pairs can be interpreted as accelerated block preconditioned gradient (BPG) iterations in order to analyze their convergence behavior by composing known estimates. An importa
Externí odkaz:
http://arxiv.org/abs/2206.00585
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $\delta\|M\|$ in $O(n^4+n^3\log^2(n/\delta)+\log(n/\delt
Externí odkaz:
http://arxiv.org/abs/2205.06804
Let $A$ be a $d\times d$ complex self-adjoint matrix, $\mathcal{X},\mathcal{Y}\subset \mathbb{C}^d$ be $k$-dimensional subspaces and let $X$ be a $d\times k$ complex matrix whose columns form an orthonormal basis of $\mathcal{X}$. We construct a $d\t
Externí odkaz:
http://arxiv.org/abs/2012.09018
Autor:
Jia, Zhongxiao
Publikováno v:
Inverse Problems, 2020
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by white noise, the Golub-Kahan bidiagonalization based LSQR method and its mathematically equivalent CGLS, the Conjugate Gradient (CG) method applie
Externí odkaz:
http://arxiv.org/abs/2003.09259
Let $\mu_1$ be a complex number in the numerical range $W(A)$ of a normal matrix $A$. In the case when no eigenvalues of $A$ lie in the interior of $W(A)$, we identify the smallest convex region containing all possible complex numbers $\mu_2$ for whi
Externí odkaz:
http://arxiv.org/abs/2004.05288
Publikováno v:
SIAM J. MATRIX ANAL. APPL. Vol. 41, No. 2 (2020), pp. 554-572
A priori, a posteriori, and mixed type upper bounds for the absolute change in Ritz values of self-adjoint matrices in terms of submajorization relations are obtained. Some of our results prove recent conjectures by Knyazev, Argentati, and Zhu, which
Externí odkaz:
http://arxiv.org/abs/1905.06998
Autor:
Jia, Zhongxiao
Publikováno v:
Inverse Problems, 2020
LSQR and its mathematically equivalent CGLS have been popularly used over the decades for large-scale linear discrete ill-posed problems, where the iteration number $k$ plays the role of the regularization parameter. It has been long known that if th
Externí odkaz:
http://arxiv.org/abs/1811.03454
Akademický článek
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Autor:
Meurant, Gérard, Tichý, Petr
In practical conjugate gradient (CG) computations it is important to monitor the quality of the approximate solution to $Ax=b$ so that the CG algorithm can be stopped when the required accuracy is reached. The relevant convergence characteristics, li
Externí odkaz:
http://arxiv.org/abs/1810.02127
Autor:
Jia, Zhongxiao
Publikováno v:
Mathematics of Computation, 2005 Jul 01. 74(251), 1441-1456.
Externí odkaz:
https://www.jstor.org/stable/4100188