Related papers: A symbol based analysis for multigrid methods for …
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
The paper analyzes a two-grid and a multigrid method for matrices belonging to the DCT-III algebra and generated by a polynomial symbol. The aim is to prove that the convergence rate of the considered multigrid method (V-cycle) is constant…
In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space $H^2_{\mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the…
A block lower triangular Toeplitz system arising from time-space fractional diffusion equation is discussed. For efficient solutions of such the linear system, the preconditioned biconjugate gradient stabilized method and flexible general…
Tensor structured Markov chains are part of stochastic models of many practical applications, e.g., in the description of complex production or telephone networks. The most interesting question in Markov chain models is the determination of…
This paper investigates non-coherent detection of single-input multiple-output (SIMO) systems over block Rayleigh fading channels. Using the Kullback-Leibler divergence as the design criterion, we formulate a multiple-symbol constellation…
Given a multigrid procedure for linear systems with coefficient matrices $A_n$, we discuss the optimality of a related multigrid procedure with the same smoother and the same projector, when applied to properly related algebraic problems…
Many fascinating systems suffer from a severe (complex action) sign problem preventing us from calculating them with Markov Chain Monte Carlo simulations. One promising method to alleviate the sign problem is the transformation of the…
In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order…
By applying the linearly implicit conservative difference scheme proposed in [D.-L. Wang, A.-G. Xiao, W. Yang. J. Comput. Phys. 2014;272:670-681], the system of repulsive space fractional coupled nonlinear Schr\"odinger equations leads to a…
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on…
The Local Fourier analysis (LFA) is a classic tool to prove convergence theorems for multigrid methods (MGMs). In particular, we are interested in optimality that is a convergence speed independent of the size of the involved matrices. For…
We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then propose several structure-exploiting preconditioners to be…
In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not…
The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…
We develop a systematic sign-embedding framework of operator-output quantum algorithms for matrix equations and matrix functions. Differing from the contour-integral treatment, we start with the matrix-sign embedding route: an augmented…
This paper presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the…
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…
We provide effective algorithms for solving block tridiagonal block Toeplitz systems with $m\times m$ quasiseparable blocks, as well as quadratic matrix equations with $m\times m$ quasiseparable coefficients, based on cyclic reduction and…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…