Name
Abstract | ||
|---|---|---|
We prove a universal limit theorem for the halting time, or iteration count, of the power/inverse power methods and the QR eigenvalue algorithm. Specifically, we analyze the required number of iterations to compute extreme eigenvalues of random, positive definite sample covariance matrices to within a prescribed tolerance. The universality theorem provides a complexity estimate for the algorithms which, in this random setting, holds with high probability. The method of proof relies on recent results on the statistics of the eigenvalues and eigenvectors of random sample covariance matrices (i.e., delocalization, rigidity, and edge universality). |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/17M1110900 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
universality,eigenvalue computation,random matrix theory | Discrete mathematics,Mathematical optimization,Covariance function,Estimation of covariance matrices,Eigenvalue algorithm,Law of total covariance,Algorithm,Covariance matrix,Divide-and-conquer eigenvalue algorithm,Mathematics,Random matrix,Covariance | Journal |
Volume | Issue | ISSN |
55 | 6 | 0036-1429 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Percy Deift | 1 | 22 | 3.64 |
| Thomas Trogdon | 2 | 6 | 3.29 |