Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems

Applications of partial orderings to study of positive definiteness, monotonicity, and convergence of iterative methods for linear system

Eigenvalues and eigenvectors of symmetric matrices, case 320

Eigenvalues and eigenvectors of symmetric matrices using FORTRAN 4 subroutine

Generalized Rayleigh methods with applications to finding eigenvalues of large matrices

Generalized Rayleigh quotients for calculating eigenvalues and eigenvectors of large matrice

A note on irreducibility for linear operators on partially ordered finite dimensional vector spaces

AbstractMany of the important applications of the Perron-Frobenius theory of nonnegative matrices assume that certain matrices are irreducible. The purpose of this note is to introduce a weaker condition which can be used in place of irreducibility, even in the more general setting of linear operators on a partially ordered finite dimensional vector space. Applications to convergence theorems, comparison results, and generalized diagonal dominance conditions are given

Stable Kalman filters for processing clock measurement data

Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given

Tight estimates for convergence of some non-stationary consensus algorithms

The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of the arcs are allowed to vary as a function of time. Under the hypothesis that some spanning tree structure is preserved along time, and that some nonzero minimal weight of the information transfer along this tree is guaranteed, an estimate of the contraction rate is given. The latter is expressed explicitly as the spectral radius of some matrix depending upon the tree depth and the lower bounds on the weights.Comment: 17 pages, 5 figure

A graph-theoretic condition for irreducibility of a set of cone preserving matrices

Given a closed, convex and pointed cone K in R^n , we present a result which infers K-irreducibility of sets of K-quasipositive matrices from strong connectedness of certain bipartite digraphs. The matrix-sets are defined via products, and the main result is relevant to applications in biology and chemistry. Several examples are presented

Coupled fixed point results in cone metric spaces for -compatible mappings

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