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We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems…

Numerical Analysis · Mathematics 2019-05-13 Nicat Aliyev , Peter Benner , Emre Mengi , Matthias Voigt

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 projection subspaces are constructed iteratively by means of…

Numerical Analysis · Mathematics 2026-01-16 Mattia Manucci , Emre Mengi , Nicola Guglielmi

We are concerned with the computation of the ${\mathcal L}_\infty$-norm for an ${\mathcal L}_\infty$-function of the form $H(s) = C(s) D(s)^{-1} B(s)$, where the middle factor is the inverse of a meromorphic matrix-valued function, and…

Numerical Analysis · Mathematics 2017-06-06 Nicat Aliyev , Peter Benner , Emre Mengi , Paul Schwerdtner , Matthias Voigt

We consider the minimization or maximization of the $J$th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix Anal. Appl., 35, 699-724). This work addresses the setting…

Numerical Analysis · Mathematics 2017-06-19 Fatih Kangal , Karl Meerbergen , Emre Mengi , Wim Michiels

We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…

Numerical Analysis · Mathematics 2023-12-06 Davide Pradovera

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…

Numerical Analysis · Mathematics 2021-04-05 Ion Victor Gosea , Serkan Gugercin , Benjamin Unger

Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a…

Numerical Analysis · Mathematics 2024-02-27 Axel Séguin , Daniel Kressner

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…

Numerical Analysis · Mathematics 2020-06-11 Yousef Saad , Mohamed El-Guide , Agnieszka Międlar

To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…

Numerical Analysis · Mathematics 2011-08-30 Oksana Bihun , Austin Bren , Michael Dyrud , Kristin Heysse

This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…

Numerical Analysis · Mathematics 2021-03-10 Vassilis Kalantzis , Yuanzhe Xi , Lior Horesh

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…

Numerical Analysis · Mathematics 2013-10-08 Emre Mengi

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Machine Learning · Computer Science 2026-04-17 Vladimir Fanaskov , Vladislav Trifonov , Alexander Rudikov , Ekaterina Muravleva , Ivan Oseledets

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 poles. Consequently, the dominant poles provide information…

Numerical Analysis · Mathematics 2022-03-09 Emre Mengi

Consider an algebraic two-level method applied to the $n$-dimensional linear system $A \mathbf{x} = \mathbf{b}$ using fine-space preconditioner (i.e., ``relaxation'' or ``smoother'') $M$, with $M \approx A$, restriction and interpolation…

Numerical Analysis · Mathematics 2025-09-12 Oliver A. Krzysik , Ben S. Southworth , Golo A. Wimmer , Ahsan Ali , James Brannick , Karsten Kahl

Representation learning plays a crucial role in automated feature selection, particularly in the context of high-dimensional data, where non-parametric methods often struggle. In this study, we focus on supervised learning scenarios where…

Methodology · Statistics 2024-08-08 Bertille Follain , Francis Bach

In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay…

Numerical Analysis · Mathematics 2019-10-31 Peter Benner , Pawan Goyal , Igor Pontes Duff

In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…

Numerical Analysis · Mathematics 2025-07-03 Sven Ullmann , Tobias Ehring , Robin Herkert , Bernard Haasdonk

This work deals with approximate solution of generalized eigenvalue problem with coefficient matrix that is an affine function of d-parameters. The coefficient matrix is assumed to be symmetric positive definite and spectrally equivalent to…

Numerical Analysis · Mathematics 2025-03-12 Joanna Bisch , Antti Hannukainen

In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for…

Numerical Analysis · Mathematics 2022-12-15 Ralf Zimmermann , Ronny Bergmann
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