Morse index and determinant of block Jacobi matrices via optimal control
Stefano Baranzini, Ivan Beschastnyi
TL;DR
This paper explores the connection between block Jacobi matrices and discrete optimal control problems, introducing new algorithms to compute their spectral invariants with applications and examples.
Contribution
It introduces novel algorithms for computing spectral invariants of block Jacobi matrices using optimal control techniques, extending continuous case methods to discrete settings.
Findings
New algorithms for spectral invariant computation
Application examples demonstrating effectiveness
Extension of continuous case techniques to discrete matrices
Abstract
We describe the relation between block Jacobi matrices and minimization problems for discrete time optimal control problems. Using techniques developed for the continuous case, we provide new algorithms to compute spectral invariants of block Jacobi matrices. Some examples and applications are presented.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Optimization and Variational Analysis · Matrix Theory and Algorithms