Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix

Percy Deift; Thomas Trogdon

doi:10.1002/cpa.21715

Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix

Percy Deift, Thomas Trogdon

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove universality for the fluctuations of the halting time for the Toda algorithm to compute the largest eigenvalue of real symmetric and complex Hermitian matrices. The proof relies on recent results on the statistics of the eigenvalues and eigenvectors of random matrices (such as delocalization, rigidity, and edge universality) in a crucial way.

Original language	English (US)
Pages (from-to)	505-536
Number of pages	32
Journal	Communications on Pure and Applied Mathematics
Volume	71
Issue number	3
DOIs	https://doi.org/10.1002/cpa.21715
State	Published - Mar 2018

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.21715

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title = "Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix",

abstract = "We prove universality for the fluctuations of the halting time for the Toda algorithm to compute the largest eigenvalue of real symmetric and complex Hermitian matrices. The proof relies on recent results on the statistics of the eigenvalues and eigenvectors of random matrices (such as delocalization, rigidity, and edge universality) in a crucial way.",

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Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix

Abstract

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