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To understand the solution of a linear, time-invariant differential-algebraic equation, one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left-half plane), the…
In this paper, we propose a unified approach for solving structure-preserving eigenvalue embedding problem (SEEP) for quadratic regular matrix polynomials with symmetry structures. First, we determine perturbations of a quadratic matrix…
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of…
This paper concerns with the group zero-norm regularized least squares estimator which, in terms of the variational characterization of the zero-norm, can be obtained from a mathematical program with equilibrium constraints (MPEC). By…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…
The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
Building on previous work that provided analytical solutions to generalised matrix eigenvalue problems arising from numerical discretisations, this paper develops exact eigenvalues and eigenvectors for a broader class of $n$-dimensional…
Stochastic PDE eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic…
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…
The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…
Shape optimisation of thin-shell structures requires a flexible, differentiable geometric representation suitable for gradient-based optimisation. We propose a neural parametric representation (NRep) for the shell mid-surface based on a…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
Low-rank matrix completion (LRMC) has demonstrated remarkable success in a wide range of applications. To address the NP-hard nature of the rank minimization problem, the nuclear norm is commonly used as a convex and computationally…
Supervised artificial neural networks with the rapidity-mass matrix (RMM) inputs were studied using several Monte Carlo event samples for various pp collision processes. The study shows the usability of this approach for general event…
In our companion paper "Multidimensional rational covariance extension with applications to spectral estimation and image compression" we discussed the multidimensional rational covariance extension problem (RCEP), which has important…