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We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices.
1901
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Zhidong Bai and Y.Q. Yin, Limit of the Smallest Eigenvalue of a Large Dimensional Sample Covariance Matrix , Annals of Probability 21
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L N Trefethen and D Bau III, Numerical linear algebra , Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997
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KR Davidson and S J Szarek, Local Operator Theory, Random Matrices and Banach Spaces , Handbook of the Geometry of Banach Spaces, Elsevier, 2001, pp. 317–366
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A Edelman and B D Sutton, Tails of Condition Number Distributions , SIAM Journal on Matrix Analysis and Applications 27
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2010
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P Forrester, Log-gases and random matrices , Princeton University Press, 2010
2010
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P A Deift, G Menon, S Olver, and T Trogdon, Universality in numerical computations with random data , Proceedings of the National Academy of Sciences of the United States of America 111
2014
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N S Pillai and J Yin, Universality of covariance matrices , The Annals of Applied Probability 24
2014
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A Bloemendal, A Knowles, H-T Yau, and J Yin, On the principal components of sample covariance matrices , Probability Theory and Related Fields 164
2016
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Z. D. Bai, B. Q. Miao, and G. M. Pan, On asymptotics of eigenvectors of large sample covariance matrix , Annals of Probability 35
2007
Cited alongside, same era.
A Lytova and L Pastur, Central limit theorem for linear eigenvalue statistics of random matrices with independent entries , The Annals of Probability 37
2009
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P A Deift, G Menon, and T Trogdon, On the condition number of the critically-scaled Laguerre Unitary Ensemble , Discrete and Continuous Dynamical Systems 36
2016
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Govind Menon and Thomas Trogdon, Smoothed Analysis for the Conjugate Gradient Algorithm , Symmetry, Integrability and Geometry: Methods and Applications 12
2016
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