Related papers: A Greedy Method for Solving Classes of PDE Problem…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of the…
We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems. Using the algorithm, we obtain the set of all possible greedy solutions and…
This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…
When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the uniform norm can be used to convert inverting those fractional…
The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…
Data-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this experimental evidence, no detailed theory has yet been…
Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…
The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…
In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done…
For many popular graph metric sparsifiers, such as spanners, emulators, and preservers, simple and elegant greedy algorithms are known that achieve state-of-the-art or existentially optimal tradeoffs between size and quality. The goal of…
PDE solutions are numerically represented by basis functions. Classical methods employ pre-defined bases that encode minimum desired PDE properties, which naturally cause redundant computations. What are the best bases to numerically…
We investigate the convergence of a nonlinear approximation method introduced by Ammar et al. (J. Non-Newtonian Fluid Mech. 139:153-176, 2006) for the numerical solution of high-dimensional Fokker-Planck equations featuring in…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for…
Consider a graph with n nodes and m edges, independent edge weights and lengths, and arbitrary distance demands for node pairs. The spanner problem asks for a minimum-weight subgraph that satisfies these demands via sufficiently short paths…
Let $X$ be a Banach space and $\mathcal{K}$ be a compact subset in $X$. We consider a greedy algorithm for finding an $n$-dimensional subspace $V_n\subset X$ which can be used to approximate the elements of $\mathcal{K}$. We are interested…
In a standard NP-complete optimization problem we introduce an interpolating algorithm between the quick decrease along the gradient (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that for a…
The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively…
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the…