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Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem, and seismic data interpolation, there exists some…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based…
This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by…
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of the problem and prove the convergence together with a priori…
In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which…
A variety of optimization problems takes the form of a minimum norm optimization. In this paper, we study the change of optimal values between two incrementally constructed least norm optimization problems, with new measurements included in…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
This study presents a theoretical structure for the monocular pose estimation problem using the total least squares. The unit-vector line-of-sight observations of the features are extracted from the monocular camera images. First, the…
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…
6D pose estimation pipelines that rely on RGB-only or RGB-D data show limitations for photometrically challenging objects with e.g. textureless surfaces, reflections or transparency. A supervised learning-based method utilising…