Related papers: Convergence parameters of nonnegative block tri-di…
We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes.
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in [Bai, et al. Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as its linear…
A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve…
We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filter with rate $\sqrt{\varepsilon}$. This is achieved by a…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of…
I study partial identification of distributional parameters in triangular systems. This model consists of a nonparametric outcome equation and a selection equation. This allows for general unobserved heterogeneity and selection on…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
The article discusses the matrices of the three forms whose inversions are: tridiagonal matrix, banded matrix or block-tridiagonal matrix and their relationships with the covariance matrices of measurements of ordinary (simple) Markov…
An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…
We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric…
We propose a novel nonparametric approach for estimating the location of block boundaries (change-points) of non-overlapping blocks in a random symmetric matrix which consists of random variables having their distribution changing from one…
Cyclic reduction is a method for the solution of (block-)tridiagonal linear systems. In this note we review the method tailored to hermitian positive definite banded linear systems. The reviewed method has the following advantages: It is…
In this paper, we aim to estimate block-diagonal covariance matrices for Gaussian data in high dimension and in fixed dimension. We first estimate the block-diagonal structure of the covariance matrix by theoretical and practical estimators…
For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials with parameters on the unit circle subject to a truncation…
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to viscosity solutions. We begin by describing a fundamental…
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…