Related papers: A parameter-dependent smoother for the multigrid m…
This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Gauss-Seidel, or conjugate gradient, with initial guess being…
Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear…
The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite attractive for nearly incompressible and incompressible…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
In this paper, we deal with multiobjective composite optimization problems, where each objective function is a combination of smooth and possibly non-smooth functions. We first propose a parameter-dependent conditional gradient method to…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time, and a finite element discretization in space. The key…
The main purpose of this paper is to provide a comprehensive convergence analysis of nonlinear AMLI-cycle multigrid method for symmetric positive definite problems. Based on classical assumptions for approximation and smoothing properties,…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
Although the linear method is one of the most robust algorithms for optimizing non-linearly parametrized wavefunctions in variational Monte Carlo, it suffers from a memory bottleneck due to the fact at each optimization step a generalized…
We present novel improvements in the context of symbol-based multigrid procedures for solving large block structured linear systems. We study the application of an aggregation-based grid transfer operator that transforms the symbol of a…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…
Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably…
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…
In the present paper we concentrate on an important issue in constructing a good multigrid solver: the choice of an efficient smoother. We will introduce all-at-once multigrid solvers for optimal control problems which show robust…
The derivation of multi-step-ahead prediction models from sampled data of a linear system is considered. A dedicated prediction model is built for each future time step of interest. In addition to a nominal model, the set of all models…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
The paper considers a linear matrix inequality (LMI) that depends on a parameter varying in a compact topological space. It turns out that if a strict LMI continuously depends on a parameter and is feasible for any value of that parameter,…