Related papers: Least-squares spectral methods for ODE eigenvalue …
We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be…
In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schr\"{o}dinger equation, proving in particular a sharp Strichartz inequality for the case of odd initial data. We also describe…
In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE's) with either (or both) L2 or point-wise bounded…
The eigenvalue problem of the Laplace-Beltrami operators on curved surfaces plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve this…
It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…
Consider the optimal subspace expansion problem for the matrix eigenvalue problem $Ax=\lambda x$: Which vector $w$ in the current subspace $\mathcal{V}$, after multiplied by $A$, provides an optimal subspace expansion for approximating a…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
Eigenanalysis of differential operators, such as the Laplace operator or elastic energy Hessian, is typically restricted to a single shape and its discretization, limiting reduced order modeling (ROM). We introduce the first eigenanalysis…
A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.
The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of…
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The approach is based on the application of a recently developed…
We propose a discontinuous least squares finite element method for solving the Helmholtz equation. The method is based on the L2 norm least squares functional with the weak imposition of the continuity across the interior faces as well as…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…
In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ODE. For…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…