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Universality for the Toda algorithm to compute the largest eigenvalue of a random matrix. (English) Zbl 1454.60012

Summary: 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.

MSC:

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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