Related papers: Block Alpha-Circulant Preconditioners for All-at-O…
The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…
In this article, we derive fast and robust parallel-in-time preconditioned iterative methods for the all-at-once linear systems arising upon discretization of time-dependent PDEs. The discretization we employ is based on a Runge--Kutta…
The motivation of this paper is twofold. First, we investigate the block-diagonalization of the $z$-block circulant matrix $\mathtt{bcirc_z}(\mathcal A)$, based on this block-diagonal structure, and develop the algorithm…
Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…
We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified…
We present a randomized algorithm that, on input a symmetric, weakly diagonally dominant n-by-n matrix A with m nonzero entries and an n-vector b, produces a y such that $\norm{y - \pinv{A} b}_{A} \leq \epsilon \norm{\pinv{A} b}_{A}$ in…
In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…
The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…
Diffusion models have shown promise in learning to solve constraint optimization problems. However, they are mostly restricted to problems with binary variables and rely on graph neural networks, hindering their application to a broader…
Data assimilation algorithms combine information from observations and prior model information to obtain the most likely state of a dynamical system. The linearised weak-constraint four-dimensional variational assimilation problem can be…
We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and…
Given a block triangular matrix $M$ over a noncommutative ring with invertible diagonal blocks, this work gives two new representations of its inverse $M^{-1}$. Each block element of $M^{-1}$ is explicitly expressed via a quasideterminant…
A block alternating splitting iteration (BASI) method is presented for solving the system arising from the finite element discretization of the distributed optimal control problem with time-periodic parabolic equations. We prove that the…
This paper deals with model predictive control problems for large scale dynamical systems with cyclic symmetry. Based on the properties of block circulant matrices, we introduce a complex-valued coordinate transformation that block…
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
We study optimal diagonal preconditioning using the classical worst-case $\kappa$-condition number and the averaging-based $\omega$-condition number. For the $\kappa$-optimal preconditioning problem, we derive an affine-based pseudoconvex…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known \textit{a priori}. It is being increasingly used in bioinformatics, text analytics, etc. Previously, biclustering has…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…