Related papers: Monotonic Properties of the Least Squares Mean
Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended…
The notion of quasi-Fej\'er monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem…
The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…
We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with…
The least squares fit to a straight line, when both variables are affected by all equal uncorrelated errors, leads to very simple results for both the estimated parameters and their standard errors, of widespread applicability. In this…
Constant gain least-mean-squares (LMS) algorithms have a wide range of applications in trajectory tracking problems, but the formal convergence of LMS in mean square is not yet fully established. This work provides an upper bound on the…
We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
Hardy property of means has been extensively studied by P\'ales and Pasteczka since 2016. The core of this research is based on few of their properties: concavity, symmetry, monotonicity, repetition invariance and homogeneity (last axiom…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
We consider the problem of estimating an unknown $n_1 \times n_2$ matrix $\mathbf{\theta^*}$ from noisy observations under the constraint that $\mathbf{\theta}^*$ is nondecreasing in both rows and columns. We consider the least squares…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results.
In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff measure of a Busemann concave space is non-trivial then the space is doubling and…