Abstract: The inverse of a Vandermonde matrix has been used for signal processing, polynomial interpolation, curve fitting, wireless communication, and system identification. In this paper, we propose a novel fast recursive algorithm to compute the inverse of a Vandermonde matrix. The algorithm computes the inverse of a higher order Vandermonde matrix using the available lower order inverse mat...

Results on the inverse interval matrix, both theoretical and computational, are surveyed. Described are, among others, formulae for the inverse interval matrix, NP-hardness of its computation, various classes of interval matrices for which the inverse can be given explicitly, and closed-form formulae for an enclosure of the inverse.

In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...

If A and B are a pair of invertible matrices of the same size, then the product AB is nonsingular, too, and the inverse of the product AB satisfies the reverse-order law (AB)−1 = B−1A−1. This law can be used to find the properties of (AB)−1, as well as to simplify various matrix expressions that involve the inverse of a matrix product. However, this formula cannot trivially be extended to the M...

The Moore-Penrose inverse of a real matrix having no square submatrix with two or more diagonals is described in terms of bipartite graphs. For such a matrix, the sign of every entry of the Moore-Penrose inverse is shown to be determined uniquely by the signs of the matrix entries; i.e., the matrix has a signed generalized inverse. Necessary and sufficient conditions on an acyclic bipartite gra...

Mineral metabolism abnormalities, such as low 1,25-dihydroxyvitamin D (1,25(OH)(2)D) and elevated parathyroid hormone (PTH), are common at even higher glomerular filtration rate than previously described. Levels of 25-hydroxyvitamin D (25(OH)D) show an inverse correlation with those of intact PTH and phosphorus. Studies of the general population found much higher all-cause and cardiovascular (C...