Related papers: Generalized Filtering Decomposition
The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
The objective of this paper is to establish the decomposition theorem for supermartingales under the $G$-framework. We first introduce a $g$-nonlinear expectation via a kind of $G$-BSDE and the associated supermartingales. We have shown…
In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of ${\cal O}(N)$ elements, we present a construction of an auxiliary coarse grid hierarchy on which a geometric…
Factoring a matrix into two low rank matrices is at the heart of many problems. The problem of matrix completion especially uses it to decompose a sparse matrix into two non sparse, low rank matrices which can then be used to predict…
When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In this paper, a recursive sparse LU decomposition for matrices…
We propose an unconditionally robust and highly effective preconditioner for general symmetric positive definite (SPD) matrices based on structured incomplete factorization (SIF), called enhanced SIF (eSIF) preconditioner. The original SIF…
{In [X. L. Lin, M. K. Ng, and Y. Zhi. {\it J. Comput. Phys.}, 434 (2021), pp. 110221] and [Y. L. Zhao, J. Wu, X. M. Gu, and H. Li. {\it Comput. Math. Appl.}, 148(2023), pp. 200--210]}, two-sided preconditioning techniques are proposed for…
The Electric Field Integral Equation (EFIE) is notorious for its ill-conditioning both in frequency and h-refinement. Several techniques exist for fixing the equation conditioning problems based on hierarchical strategies, Calderon…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
The convergence behavior of classical iterative solvers for parametric partial differential equations (PDEs) is often highly sensitive to the domain and specific discretization of PDEs. Previously, we introduced hybrid solvers by combining…
In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…
This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…
The investigation of width parameters in both graph and algebraic contexts has attracted considerable interest. Among these parameters, the linear branch width has emerged as a crucial measure. In this concise paper, we explore the concept…
Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…
While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…