相关论文: Propagation of Errors for Matrix Inversion

How to calculate the exponential of matrices in an explicit manner is one of fundamental problems in almost all subjects in Science. Especially in Mathematical Physics or Quantum Optics many problems are reduced to this calculation by…

The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling…

The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The…

Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…

Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The…

The numerical analysis of gradient inclusions in a compact subset of $2\times 2$ diagonal matrices is studied. Assuming that the boundary conditions are reached after a finite number of laminations and using piecewise linear finite…

We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global errors. We derive upper bounds for the global error, and show…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and…

The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…

We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation…

A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier…

Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…

The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic…

We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…

A novel approach for solving linear estimation problem in multi-user massive MIMO systems is proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the dot product. The general…

We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…