On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem

Andrew Knyazev, A.L. Shorokhodov

Type: Article

Publication Date: 1991-08-01

Citations: 26

DOI: https://doi.org/10.1016/0024-3795(91)90379-b

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Linear Algebra and its Applications - View

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Works That Cite This (20)

Action	Title	Year	Authors
+	On convergence of iterative projection methods for symmetric eigenvalue problems	2016	Kensuke Aishima
+	A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems	2002	Andrew Knyazev Klaus Neymeyr
+ PDF Chat	Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation	2023	Ming Zhou Zhaojun Bai Yunfeng Cai Klaus Neymeyr
+	Geodesic Convexity of the Symmetric Eigenvalue Problem and Convergence of Steepest Descent	2024	Foivos Alimisis Bart Vandereycken
+	Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems	2015	Ren‐Cang Li
+	Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method	2001	Andrew Knyazev
+	Convergence estimates of nonrestarted and restarted block‐Lanczos methods	2018	Ming Zhou
+	An unconstrained global optimization framework for real symmetric eigenvalue problems	2019	Yunho Kim
+	Efficient solution of symmetric eigenvalue problems using multigridpreconditioners in the locally optimal block conjugate gradient method	2001	Andrew Knyazev Klaus Neymeyr
+	Global convergence of the restarted Lanczos and Jacobi–Davidson methods for symmetric eigenvalue problems	2015	Kensuke Aishima

Works Cited by This (5)

Action	Title	Year	Authors
+	Convergence rate estimates for iterative methods for a mesh symmetrie eigenvalue problem	1987	Andrew Knyazev
+	The Symmetric Eigenvalue Problem	1998	Beresford Ν. Parlett
+	Sharp a priori error estimates of the Rayleigh-Ritz method without assumptions of fixed sign or compactness	1985	Andrew Knyazev
+	Supplement to chapter VII	1991	Yu. L. Dalecky N. Yu. Goncharuk
+	The Symmetric Eigenvalue Problem.	1981	J. H. Wilkinson Beresford Ν. Parlett