The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix

Name: The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix
Brand: Cambridge University Press
Availability: OutOfStock
Rating: 5 (1 reviews)

By Percy Deift

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Description

Written by leaders in the field, this text showcases some of the remarkable properties of the finite Toda lattice and applies this theory to establish universality for the associated Toda eigenvalue algorithm for random Hermitian matrices. The authors expand on a 2019 course at the Courant Institute to provide a comprehensive introduction to the area, including previously unpublished results. They begin with a brief overview of Hamiltonian mechanics and symplectic manifolds, then derive the action-angle variables for the Toda lattice on symmetric matrices. This text is one of the first to feature a new perspective on the Toda lattice that does not use the Hamiltonian structure to analyze its dynamics. Finally, portions of the above theory are combined with random matrix theory to establish universality for the runtime of the associated Toda algorithm for eigenvalue computation.

Product details

Binding:: Paperback
Number of Pages:: 172
Release Date:: 2025-10-06
Publication Date:: 2025-10-06
Publisher:: Cambridge University Press
Languages:: Original: English
ISBN10:: 1009664352
ISBN13:: 9781009664356
GPSR Manufacturer Reference:: [email protected]
Weight:: 259 g
Height:: 152 cm
Width:: 229 cm
Thickness:: 10 cm

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