In this article we apply proper splittings of matrices to develop an iterative process approximate solutions matrix equations the form TX=W. Moreover, by using partial order induced positive semidefinite matrices, obtain equivalent conditions convergence process. We also include some speed comparison results method. addition, for all T propose a splitting based on polar decomposition T.

We investigate relations between (+, ) vector products for binary integer functions . We show that there exists a broad class of products that are equivalent under one-to-polylog reductions to the computation of the Hamming distance. Examples include, but are not exhausted by: the dominance product, the threshold product and `2p+1 distances for constant p. Our result has the following consequen...

An explicit description is giv e n for th e uniqu e gra ph with as few arcs (eac h bearin g a positive length) as pos s ibl e, whi c h has a presc rib ed mat rix of s hortest-p ath di stan ces be twee n pa irs of distinct vertices. The sam e is d one in th e case wh e n the ith diago na l matrix e ntr y, in s te ad o f be ing zero , represents th e. le ngth of a s hort est c losed path co ntain...

In this paper, we use known bounds on the smallest eigenvalue of a symmetric matrix and Schoenberg’s Theorem to provide both necessary as well as sufficient trace inequalities that guarantee a matrix D is a Euclidean distance matrix, EDM. We also provide necessary and sufficient trace inequalities that guarantee a matrix D is an EDM generated by a regular figure.

Consider the problem of determining whether or not a partial dissimilarity matrix can be completed to a Euclidean distance matrix. The dimension of the distance matrix may be restricted and the known dissimilarities may be permitted to vary subject to bound constraints. This problem can be formulated as an optimization problem for which the global minimum is zero if and only if completion is po...

Euclidean Distance Matrix Analysis (EDMA) of form is a coordinate free approach to the analysis o f form using landmark data. In this paper, the problem of estimation of mean form, variancecovariance matrix, and mean form difference under the Gaussian perturbation model is considered using EDMA. The suggested estimators are based on the method of moments. They are shown to be consistent, that i...