We investigate the rewrite relation over graphs induced by constructor-based weakly orthogonal graph rewriting systems. It is well known that this relation is not confluent in general whereas it is confluent in the case of weakly orthogonal term rewriting systems. We show, however, that the considered relation is always confluent, as well as confluent modulo bisimilarity, for a large class of g...

For n × n Vandermonde matrix Vn = (αi−1 j )1≤i j≤n with translated Chebyshev zero nodes, it is discovered that V T n admits an explicit QR decomposition with the R-factor consisting of the coefficients of the translated Chebyshev polynomials of degree less than n. This decomposition then leads to an exact expression for the condition number of its submatrix Vk,n = (αi−1 j )1≤i≤k,1≤j≤n (so-calle...

In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde matrix VR(x) = [rj−1(xi)] with polynomials {rk(x)} related to a Hessenberg quasiseparable matrix. The result generalizes the well-known Björck-Pereyra algorithm for classical Vandermonde systems involving monomials. It also generalizes the algorithms of [RO91] for VR...

The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We exte...

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