The Fast Pole-Zero (ARMA) Recursive Least Squares Algorithm is derived using geometric projections. The new algorithm has a reduced number of computations compared to the algorithm obtained using matrix methods. In particular two inner products are eliminated. This is particularly important in multiprocessor implementations of the algorithm. The geometric approach provides insight and useful in...

Given a complex matrix H, we consider the decomposition H=QRP∗ where Q and P have orthonormal columns, and R is a real upper triangular matrix with diagonal elements equal to the geometric mean of the positive singular values of H. This decomposition, which we call the geometric mean decomposition, has application to signal processing and to the design of telecommunication networks. The unitary...

For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might involve exceptional points, we construct an appropriate parameter space M and a lines bundle Ln over M such that the adiabatic geometric phases associated with the eigenstates of the initial Hamiltonian coincide with the holonomies of Ln. We examine the case of 2× 2 matrix Hamiltonians in detail and show that, contrary to ...

1. Introduction: In the research area of one dimensional stochastic processes, Markov chains acquire special importance due to large number of applications. One of the simplest possible continuous time Markov chains, namely birth-and-death process arises naturally in many queueing models. Such a Markov chain has an efficient recursive solution for the equilibrium probabilities. Specifically the...

In our previous paper we have discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In this paper we consider the case of a general matrix of transition exponents. Our leading idea that a relevant geometric object in this case is a certain closed 2-form compatible with the cluster algebra structure. The main example is...

In the previous paper [GSV] we have discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In this paper we consider the case of a general matrix of transition exponents. Our leading idea is that a relevant geometric object in this case is a certain closed 2-form compatible with the cluster algebra structure. The main e...