Related papers: Incorporating Fixed-Pole Information in the Data-D…
The present paper continues our investigation of an implementation of a least-squares collocation method for higher-index differential-algebraic equations. In earlier papers, we were able to substantiate the choice of basis functions and…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed guaranteed computation methods for both eigenvalues and…
In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be…
This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
We introduce a direct numerical treatment of nonlinear higher-index differential-algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard…
The pooling of prior opinions is an important area of research and has been for a number of decades. The idea is to obtain a single belief probability distribution from a set of expert opinion belief distributions. The paper proposes a new…
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g. the Helmholtz…
This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem with homogeneous Dirichlet boundary conditions. In particular, the resulting error estimator constitutes an upper bound…
A new general framework is presented for implementing complex a priori knowledge, having in mind especially situations where the number of available training data is small compared to the complexity of the learning task. A priori…
Estimating pose from given 3D correspondences, including point-to-point, point-to-line and point-to-plane correspondences, is a fundamental task in computer vision with many applications. We present a complete solution for this task,…
Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…
This paper introduces a novel method for solving the single-source localization problem, specifically addressing the case of trilateration. We formulate the problem as a weighted least-squares problem in the squared distances and…
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 derive optimal and asymptotically exact a posteriori error estimates for the approximation of the Laplace eigenvalue problem. To do so, we combine two results from the literature. First, we use the hypercircle techniques developed for…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
We consider the problem of fitting a set of points in Euclidean space by an algebraic hypersurface. We assume that points on a true hypersurface, described by a polynomial equation, are corrupted by zero mean independent Gaussian noise, and…