Related papers: On the matching of eigensolutions to parametric pa…
In this article, we describe an implementation of a polynomial system solver to compute the approximate solutions of a 0-dimensional polynomial system with finite precision p-adic arithmetic. We also describe an improvement to an algorithm…
Given two real symmetric matrices, their eigenvalue configuration is the relative arrangement of their eigenvalues on the real line. In this paper, we consider the following problem: given two parametric real symmetric matrices and an…
We consider parameterized variational inverse problems that are constrained by partial differential equations (PDEs). We seek to efficiently compute the solution of the inverse problem when auxiliary model parameters, which appear in the…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
In the aim of reducing the computational cost of the resolution of parameter-dependent eigenvalue problems, a model order reduction (MOR) procedure is proposed. We focus on the case of non-self-adjoint generalized eigenvalue problems, such…
We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…
This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…
In this paper, we study the partial pole assignment problem in symmetric quadratic pencil with time delay. A novel multi-step method is proposed to solve this problem, resulting in the undesired eigenvalues being moved to desired values,…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…