Related papers: Structure-preserving deflation of critical eigenva…
Cubic forms in three variables are parametrised by points of $\P^9$. We study the subvarieties in this space defined by decomposable forms. Specifically, we calculate the equivariant minimal resolutions of these varieties and describe their…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where internal measurements are available from a reduced number of…
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differential equations have invariants, and numerical schemes for…
We propose a method to determine the quantum phase boundaries of one-dimensional systems using sine-square deformation (SSD). Based on the proposition, supported by several exactly solved cases though not proven in full generality, that "if…
We explore the concept of eigenvalue avoidance, which is well understood for real symmetric and Hermitian matrices, for other classes of structured matrices. We adopt a differential geometric perspective and study the generic behaviour of…
We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural vibration which we model as a second-order differential eigenvalue problem. The dispersion-minimized mass reduces the eigenvalue error…
In this paper, we introduce a Helmholtz-type decomposition for the space of square integrable, symmetric-matrix-valued functions analogous to the standard Helmholtz decomposition for vector fields. This decomposition provides a better…
The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. In this paper, using the shape difference quotient of eigenvalues, we propose a stable computation…
The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
The Duffing oscillator describes the dynamics of a mass suspended on a spring with position-dependent stiffness. The mass is assumed to experience a linear damping and a time-dependent external forcing. The model has been instrumental in…
A common algorithm for the computation of eigenvalues of real symmetric tridiagonal matrices is the iteration of certain special maps $F_\sigma$ called shifted $QR$ steps. Such maps preserve spectrum and a natural common domain is ${\cal…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally…
This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on a scalar parameter.…
We compute the form factors of the order and disorder operators, together with those of the stress-energy tensor, of the two-dimensional three-state Potts model with vacancies along its thermal deformation of the critical point. At…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…