Related papers: Multigrid methods for Toeplitz linear systems with…
Reduction multigrids have recently shown good performance in hyperbolic problems without the need for Gauss-Seidel smoothers. When applied to the hyperbolic limit of the Boltzmann Transport Equation (BTE), these methods result in very close…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…
In this paper, we study the optimization problem on a compact matrix manifold. While existing feasible algorithms can be broadly categorized into retraction-based and projection-based methods, compared to the more comprehensive and in-depth…
Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
This paper proposes a generalization of the conjugate gradient (CG) method used to solve the equation $Ax=b$ for a symmetric positive definite matrix $A$ of large size $n$. The generalization consists of permitting the scalar control…
We analyse the convergence of the ergodic formula for Toeplitz matrix-sequences generated by a symbol and we produce explicit bounds depending on the size of the matrix, the regularity of the symbol and the regularity of the test function.
We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…
We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…
Toeplitz matrices for the study of the fractional Laplacian on a bounded interval. In this work we get a deep link between (--$\Delta$) $\alpha$ ]0,1[ the fractional Laplacian on the interval ]0, 1[ and T N ($\Phi$ $\alpha$) the Toeplitz…
We present SymPix, a special-purpose spherical grid optimized for efficient sampling of rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…