The public key cryptosystems MST1 and MST2 make use of certain kinds of factorizations of finite groups. We show that generalizing such factorizations to infinite groups allows a uniform description of several proposed cryptographic primitives. In particular, a generalization of MST2 can be regarded as a unifying framework for several suggested cryptosystems including the ElGamal public key sys...

The paper gives a self-contained survey of fast algorithms for solving linear systems of equations with Toeplitz or Hankel coefficient matrices. It is written in the style of a textbook. Algorithms of Levinson-type and of Schur-type are discussed. Their connections with triangular factorizations, Padè recursions and Lanczos methods are demonstrated. In the case in which the matrices possess add...

Consider factorizations into transpositions of an n-cycle in the symmetric group Sn. To every such factorization we assign a monomial in variables wij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-fac...

We provide a bijection between the set of factorizations, that is, ordered (n− 1)-tuples of transpositions in Sn whose product is (12...n), and labelled trees on n vertices. We prove a refinement of a theorem of Dénes [3] that establishes new tree-like properties of factorizations. In particular, we show that a certain class of transpositions of a factorization correspond naturally under our bi...

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include flattening the data and applying matrix factorizations such as principal components analysis (PCA) or employing tensor decompositions such as the CANDECOMP / P...

Several matrix factorizations depend on orthogonal factors, matrices that preserve the Euclidean scalar product. Some of these factorizations can be extended and generalized to (J, J̃)-orthogonal factors, that is, matrices that satisfy H JH = J̃ , where J and J̃ are diagonal with diagonal elements ±1. The purpose of this work is to analyze the perturbation of matrix factorizations that have a (J, ...

Increasing performance demands in control applications necessitate accurate modeling of complex systems for control. The aim of this chapter is to develop a new system identification algorithm that delivers models that are suitable for subsequent robust control and can be reliably applied to complex systems. To achieve this, an identification algorithm is developed that delivers system model in...

Within a lattice approach, the purpose of this paper is to give general necessary and sufficient conditions for internal stabilizability and for the existence of (weakly) left-/right-/doubly coprime factorizations of multi input multi output linear systems. These results extend the ones recently obtained in [24] for single input single output systems. In particular, combining these results with...

We show that in certain Prüfer domains, each nonzero ideal I can be factored as I = I v Π, where I v is the divisorial closure of I and Π is a product of maximal ideals. This is always possible when the Prüfer domain is h-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the h-local property in Prüfer domains. We also explore ...

On the basis of a new WY -like representation block algorithms for orthogonal symplectic matrix factorizations are presented. Special emphasis is placed on symplectic QR and URV factorizations. The block variants mainly use level 3 (matrix-matrix) operations that permit data reuse in the higher levels of a memory hierarchy. Timing results show that our new algorithms outperform standard algorit...