Related papers: A Robust Algebraic Domain Decomposition Preconditi…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain…
Many computer vision applications require robust and efficient estimation of camera geometry from a minimal number of input data measurements, i.e., solving minimal problems in a RANSAC framework. Minimal problems are usually formulated as…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the…
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…
We propose an operator preconditioner for general elliptic pseudodifferential equations in a domain $\Omega$, where $\Omega$ is either in $\mathbb{R}^n$ or in a Riemannian manifold. For linear systems of equations arising from low-order…
Techniques based on $k$-th order Hodge Laplacian operators $L_k$ are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplicial complexes. In all of them, it is required to solve a…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major…
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…
We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
Random Feature Methods (RFMs) and their variants such as extreme learning machine finite-basis physics-informed neural networks (ELM-FBPINNs) offer a scalable approach for solving partial differential equations (PDEs) by using localized,…
Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…