This paper presents two matrix factorizations for recursive pruned discrete cosine transforms. Both factorizations have lower computational complexity when compared to the method of El-Sharkawy and Eshmawy (1995). ( 1998 Elsevier Science B.V. All rights reserved.

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for finding patterns from the data. Rather than using the standard algebra – and the summation of the rank-1 components to build the approximation of the original ma...

This is a survey of recently published results. We introduce and study a wide class algebras associated to directed graphs and related to factorizations of noncommutative polynomials. In particular, we show that for many well-known graphs such algebras are Koszul and compute their Hilbert series. Let R be an associative ring with unit and P (t) = a0t +a1t +· · ·+an be a polynomial over R. Here ...

Minimal transitive cycle factorizations, parking functions and labeled trees are related very closely. Using the correspondences between them, we find a refined enumeration of minimal transitive factorizations of permutations of type (1, n− 1) and (2, n− 2).

Minimal transitive cycle factorizations and parking functions are related very closely. Using the correspondence between them, we find a bijection between minimal transitive factorizations of permutations of type (1, n − 1) and prime parking functions of length n.

The automorphism group AutfSy of the full 2-shift is conjectured to be generated by the shift and involutions. We approach this problem by studying a certain family of automorphisms whose order was unknown, but which we show to be finite and for which we find factorizations as products of involutions. The result of this investigation is the explicit construction of a subgroup %Z of Aut(Z2) ; %Z...

The Fast Fourier Transform (FFT) is based on an important factorization of the Fourier matrix Fn into a product of sparse matrices. In this paper, we demonstrate the existence of a set of FFT-like factorizations for an arbitrary Kronecker product of Fourier matrices F = Fn1 ⊗ . . . ⊗ Fnk . We show that there exists such a factorization for any chain of nested subgroups of the Abelian group Zn1×...

We continue the study of the so-called thematic factorizations of admissible very badly approximable matrix functions. These factorizations were introduced by V.V. Peller and N.J. Young for studying superoptimal approximation by bounded analytic matrix functions. Even though thematic indices associated with a thematic factorization of an admissible very badly approximable matrix function are no...