60 citations · 75 across the 13 of their papers we have counts for
18 papers
Approximation of the Pseudospectral Abscissa via Eigenvalue Perturbation Theory
Waqar Ahmed, Emre Mengi
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergen…
Uniform Approximation of Eigenproblems of a Large-Scale Parameter-Dependent Hermitian Matrix
Mattia Manucci, Emre Mengi, Nicola Guglielmi
We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The…
Minimization of the Pseudospectral Abscissa of a Quadratic Matrix Polynomial
Volker Mehrmann, Emre Mengi
For a quadratic matrix polynomial dependent on parameters and a given tolerance , the minimization of the -pseudospectral abscissa over the set of permissible parameter va…
A Subspace Framework for Model Reduction
Emre Mengi
We consider the problem of locating a nearest descriptor system of prescribed reduced order to a descriptor system with large order with respect to the norm.…
Large-Scale Minimization of the Pseudospectral Abscissa
Nicat Aliyev, Emre Mengi
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability an…
Large-Scale Estimation of Dominant Poles of a Transfer Function by an Interpolatory Framework
Emre Mengi
We focus on the dominant poles of the transfer function of a descriptor system. The transfer function typically exhibits large norm at and near the imaginary parts of the dominant…
Derivative Interpolating Subspace Frameworks for Nonlinear Eigenvalue Problems
Rifqi Aziz, Emre Mengi, Matthias Voigt
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of…
A Subspace Framework for -Norm Minimization
Nicat Aliyev, Peter Benner, Emre Mengi +1
We deal with the minimization of the -norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Sub…
Computation of Stability Radii for Large-Scale Dissipative Hamiltonian Systems
Nicat Aliyev, Volker Mehrmann, Emre Mengi
A linear time-invariant dissipative Hamiltonian (DH) system x' = (J-R)Q x, with a skew-Hermitian J, an Hermitian positive semi-definite R, and an Hermitian positive definite Q, is…
Nonsmooth Rate-of-Convergence Analyses of Algorithms for Eigenvalue Optimization
Fatih Kangal, Emre Mengi
Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitia…
Large-Scale and Global Maximization of the Distance to Instability
Emre Mengi
The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the l…
Subspace Methods for 3-Parameter Eigenvalue Problems
Michiel E. Hochstenbach, Karl Meerbergen, Emre Mengi +1
We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular exam…
Large-Scale Computation of -Norms by a Greedy Subspace Method
Nicat Aliyev, Peter Benner, Emre Mengi +2
We are concerned with the computation of the -norm for an -function of the form , where the middle factor is t…
A Subspace Method for Large Scale Eigenvalue Optimization
Fatih Kangal, Karl Meerbergen, Emre Mengi +1
We consider the minimization or maximization of the th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix An…
A Support Based Algorithm for Optimization with Eigenvalue Constraints
Emre Mengi
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of w…
Matrix Polynomials with Specified Eigenvalues
Michael Karow, Emre Mengi
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. P…
Numerical Optimization of Eigenvalues of Hermitian Matrix Functions
Emre Mengi, Emre Alper Yildirim, Mustafa Kilic
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters…
Generalized Eigenvalue Problems with Specified Eigenvalues
Daniel Kressner, Emre Mengi, Ivica Nakic +1
We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value opt…