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The Vandermonde matrix is ubiquitous in mathematics and engineering. Both the Vandermonde matrix and its inverse are often encountered in control theory, in the derivation of numerical formulas, and in systems theory. In some cases block vandermonde matrices are used. Block Vandermonde matrices, considered in this paper, are constructed from a full set of solvents of a corresponding matrix polynomial. These solvents represent block poles and block zeros of a linear multivariable dynamical time-invariant system described in matrix fractions. Control techniques of such systems deal with the inverse or determinant of block vandermonde matrices. Methods to compute the inverse of a block vandermonde matrix have not been studied but the inversion of block matrices (or partitioned matrices) is very well studied. In this paper, properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. A parallelization of these algorithms is also presented. The proposed algorithms are validated by a comparison based on algorithmic complexity.

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The ubiquitous computing and context-aware applications experience at the present time a very important development. This has led organizations to open more of their information systems, making them available anywhere, at any time and integrating the dimension of mobile users. This cannot be done without taking into account thoughtfully the access security: a pervasive information system must henceforth be able to take into account the contextual features to ensure a robust access control. In this paper, access control and a few existing mechanisms have been exposed. It is intended to show the importance of taking into account context during a request for access. In this regard, our proposal incorporates the concept of trust to establish a trust relationship according to three contextual constraints (location, social situation and time) in order to decide to grant or deny the access request of a user to a service.