Related papers: Partial condition number for the equality constrai…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
For the numerical solution of the cubic nonlinear Schr\"{o}dinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to…
The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…
This paper explores preconditioning the normal equation for non-symmetric square linear systems arising from PDE discretization, focusing on methods like CGNE and LSQR. The concept of ``normal'' preconditioning is introduced and a strategy…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the $\ell_1$-norm of the part of the solution vector which is known to be sparse. Such a problem is closely…
We give sharp regularity results for the solution to the stochastic wave equation with linear fractional-colored noise. We apply these results in order to establish upper and lower bound for the hitting probabilities of the solution in…
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 derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations.…
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their…
Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
In this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalue computations? In this note we answer this question with…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
We consider a linear equation $\partial_t u = \mathcal{L}u$, where $\mathcal{L}$ is a generator of a semigroup of linear operators on a certain Hilbert space related to an initial condition $u(0)$ being a generalised stationary random field…