First order sensitivity analysis of symplectic eigenvalues

Authors

Hemant Kumar Mishra, Indian Statistical Institute (Delhi Centre)

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

Abstract

For every 2n×2n positive definite matrix A there are n positive numbers d1(A)≤…≤dn(A) associated with A called the symplectic eigenvalues of A. It is known that dm are continuous functions of A but are not differentiable in general. In this paper, we show that the directional derivative of dm exists and derive its expression. We also discuss various subdifferential properties of dm such as Clarke and Michel-Penot subdifferentials.

First Page

324

Last Page

345

DOI

10.1016/j.laa.2020.07.003

Publication Date

11-1-2020

Comments

Open Access, Green

Recommended Citation

Mishra, Hemant Kumar, "First order sensitivity analysis of symplectic eigenvalues" (2020). Journal Articles. 89.
https://digitalcommons.isical.ac.in/journal-articles/89