This paper discusses random linear network coding with and without the use of a Vandermonde matrix to obtain the coding coefficients. Performance comparisons of such random linear network coded networks with networks employing traditional store and forward technique are also provided. It is shown that random linear network coding using a Vandermonde matrix can improve the network utilization fa...

The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein–Vandermonde matrix is considered. Bernstein–Vandermonde matrices are a generalization of Vandermonde matrices arising when considering for the space of the algebraic polynomials o...

The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein–Vandermonde matrix is considered. Bernstein–Vandermonde matrices are a generalization of Vandermonde matrices arising when considering for the space of the algebraic polynomials o...

It is shown that an innnite Hankel matrix of a nite rank (or a nite Hankel matrix) admits a generalized Vandermonde decomposition H = V T DV , where V is a generalized Vandermonde matrix, and D is a block diagonal matrix. The full structure of this decomposition was rst fully discussed by Vandevoorde 9], but the development here is based solely on linear algebra considerations, speciically the ...

A scaled version of the lower and the upper triangular factors of the inverse of the Vandermonde matrix is given. Two applications of the q-Pascal matrix resulting from the factorization of the Vandermonde matrix at the q-integer nodes are introduced. c © 2007 Elsevier Ltd. All rights reserved.

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Due to their remarkable application in many branches of applied mathematics such as combinatorics, coding theory, and cryptography, Vandermonde matrices have received a great amount of attention. Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. Lacan and Fimes introduc...