Mert Gürbüzbalaban

Fast Approximation of the

The

H_\infty

H_\infty

Norm via Optimization over Spectral Value Sets

norm of a transfer matrix function for a control system is the reciprocal of the largest value of

On the Convergence Rate of Incremental Aggregated Gradient Algorithms

\varepsilon

A globally convergent incremental Newton method

such that the associated

Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint

\varepsilon

Global Convergence Rate of Proximal Incremental Aggregated Gradient Methods

-spectral value set is contained in the stability region for the dynamical system (the left half-plane in the continuous-time case and the unit disk in the discrete-time case). After deriving some fundamental properties of spectral value sets, particularly the intricate relationship between the singular vectors of the transfer matrix and the eigenvectors of the corresponding perturbed system matrix, we extend an algorithm recently introduced by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166--1192] for approximating the maximal real part or modulus of points in a matrix pseudospectrum to spectral value sets, characterizing its fixed points. We then introduce a Newton-bisection method to approximate the

Some Regularity Results for the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix

H_\infty

Explicit solutions for root optimization of a polynomial family

norm, for which each step requires optimization of the real part or the modulus over an

Surpassing Gradient Descent Provably: A Cyclic Incremental Method with Linear Convergence Rate

\varepsilon