A new approach to assess the orthogonality of two-dimensional (2-D) separation systems based on conditional entropy is developed. It considers the quantitative distribution of peaks in the entire separation space such that the orthogonality obtained is independent of the number of peaks observed for each separation technique. Therefore, it can be used to compare the orthogonality of different 2...

For frequency hypercubes of dimension d > 2, we discuss several generalizations of the usual notion of pairwise orthogonality. We provide some constructions for complete sets of orthogonal frequency hypercubes. 1. Strong orthogonality for frequency hypercubes In this paper we will examine strong forms of orthogonality for frequency hypercubes. The standard de nition requires that each ordered p...

The paper examines the impact of Rician fading on the orthogonality of dual-polarized MIMO channels in a measured urban macrocellular scenario. The measurements confirm the previous finding that the Rician K-factors of the crosspolarized channels are strongly correlated to those of the copolarized channels. However, the Rician K-factors do not in general give direct indications on the orthogona...

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

We show that limit transitions from Askey-Wilson polynomials to q-Racah, little and big q-Jacobi polynomials can be made rigorous on the level of their orthogonality measures in a suitable weak sense. This allows us to derive the orthogonality relations and norm evaluations for the q-Racah polynomials, little and big q-Jacobi polynomials by taking limits in the orthogonality relations and norm ...

We introduce iterative methods named TriCG and TriMR for solving symmetric quasi-definite systems based on the orthogonal tridiagonalization process proposed by Saunders, Simon Yip in 1988. are tantamount to preconditioned Block-CG Block-MINRES with two right-hand sides which approximate solutions summed at each iteration, but require less storage work per iteration. evaluate performance of lin...

A randomized Gram--Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical while being at least as numerically stable modified process. Our approach based on random sketching, which a dimension reduction technique consisting in estimation inner products by their small eff...