The Schur class, denoted by $${\mathcal {S}}({\mathbb {D}})$$ , is the set of all functions analytic and bounded one in modulus open unit disc $${\mathbb {D}}$$ complex plane {C}}$$ that $$\begin{aligned} {\mathcal {D}}) = \left\{ \varphi \in H^\infty ({\mathbb {D}}): \Vert _{\infty } := \sup _{z {\mathbb {D}}} |\varphi (z)| \le 1\right\} . \end{aligned}$$ elements are called functions. A class...

We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error. The main ingredient is an exact factorization algorithm when the rows and columns of the factors are constrained to lie in a general polyhedron. This strictly...

Motivated by a 40-year-old problem due to Peter Cameron on extending partial parallelisms, we provide necessary and sufficient conditions under which one can extend an r-factorization of a complete 3-uniform hypergraph on m vertices, K3 m, to an s-factorization of K3 n. This generalizes an existing result of Baranyai and Brouwer–where they proved it for the case r = s = 1.

We propose general computational procedures based on descriptor state-space realizations to compute coprime factorizations of rational matrices with minimum degree denominators. Enhanced recursive pole dislocation techniques are developed, which allow to successively place all poles of the factors into a given “good” domain of the complex plane. The resulting McMillan degree of the denominator ...

This Report updates the tables of factorizations of an±1 for 13 ≤ a < 100, previously published asCWI Report NM-R9212 (June 1992) and updated in CWI Report NM-R9419 (Update 1, September1994) and CWI Report NM-R9609 (Update 2, March 1996). A total of 951 new entries in the tablesare given here. The factorizations are now complete for n < 76, and there are no composite cofactorssm...