Thomas Trogdon – författare
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2 produkter
2 produkter
Del 500 - London Mathematical Society Lecture Note Series
The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix
Häftad, Engelska, 2025
786 kr
Skickas inom 7-10 vardagar
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on a 2019 course at the Courant Institute to provide a comprehensive introduction to the area, including previously unpublished results.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.
Häftad, Engelska, 2015
1 165 kr
Skickas inom 5-8 vardagar
Riemann–Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann–Hilbert problem. This book, the most comprehensive one to date on the applied and computational theory of Riemann-Hilbert problems, includes:An introduction to computational complex analysis.An introduction to the applied theory of Riemann–Hilbert problems from an analytical and numerical perspective.A discussion of applications to integrable systems, differential equations, and special function theory.Six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann–Hilbert method, each of mathematical or physical significance or both.