eBook - PDF
The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix
- 174 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix
About this book
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on a 2019 course at the Courant Institute to provide a comprehensive introduction to the area, including previously unpublished results.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.
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Yes, you can access The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix by Percy Deift,Guillaume Dubach,Carlos Tomei,Thomas Trogdon in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Series page
- Title page
- Copyright page
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Hamiltonian Mechanics and Integrable Systems
- 3 The Toda Lattice
- 4 Toda without Hamiltonian Structure
- 5 Random Matrix Ensembles
- 6 Universality for the Toda Algorithm
- References
- Notations and Abbreviations
- Index