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We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$.
Superlinear convergence of randomized block Lanczos algorithm
Qiaochu Yuan, Ming Gu, and Bo Li · 1904
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Orthogonal polynomials
Gabor Szegő · 1939
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A note on a method for generating points uniformly on n-dimensional spheres
Mervin E Muller · 1959
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Estimates for some computational techniques in linear algebra
Shmuel Kaniel · 1966
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Construction of gauss-christoffel quadrature formulas
Walter Gautschi · 1968
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Some new bounds on perturbation of subspaces
Chandler Davis and William M Kahan · 1969
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The computation of eigenvalues and eigenvectors of very large sparse matrices
Christopher Conway Paige · 1971
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The block Lanczos method for computing eigenvalues
Gene Howard Golub and Richard Underwood · 1977
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Hankel forms
Gabor Szegő · 1977
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The recursive solution of the schrödinger equation
Roger Haydock · 1980
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On the rates of convergence of the Lanczos and the block-Lanczos methods
Yousef Saad · 1980
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An implicitly restarted Lanczos method for large symmetric eigenvalue problems
Daniela Calvetti, Lothar Reichel, and Danny Chris Sorensen · 1994
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Probabilistic bounds on the extremal eigenvalues and condition number by the Lanczos algorithm
Jacek Kuczyński and Henryk Woźniakowski · 1994
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Numerical linear algebra
Lloyd N. Trefethen and David Bau III · 1997
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Percy Deift · 1999
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A note on the convergence of Ritz values for sequences of matrices
Bernhard Beckermann · 2000
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Which eigenvalues are found by the Lanczos method?
Arno B. J. Kuijlaars · 2000
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On the role of sparsity in compressed sensing and random matrix theory
Roman Vershynin · 2009
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Further analysis of the Arnoldi process for eigenvalue problems
Mohammed Bellalij, Yousef Saad, and Hassane Sadok · 2010
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Numerical methods for large eigenvalue problems: revised edition
Yousef Saad · 2011
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Roger A Horn and Charles R Johnson · 2012
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Approximating spectral densities of large matrices
Lin Lin, Yousef Saad, and Chao Yang · 2016
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A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski, Chao Yang, and Yousef Saad · 2016
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