A matrix Euclidean algorithm induced by state space realization

A Matrix Euclidean Algorithm induced by State Space Realization

An eecient algorithm is developed for determining the greatest common left divisor (GCLD) of two polynomial matrices. Knowing this divisor allows for several immediate applications: In coding theory, a noncatastrophic convolutional encoder can be derived from an arbitrary one. In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found. In linear algeb...

A matrix Euclidean algorithm for minimal partial realization

A matrix Euclidean algorithm and matrix continued fraction expansions

Euclidean Algorithm for Laurent Polynomial Matrix Extension

In this paper, we develop a novel and effective Euclidean algorithm for Laurent polynomial matrix extension (LPME), which is the key of the construction of perfect reconstruction filter banks (PRFBs). The algorithm simplifies the dual-chain approach to the construction of PRFBs in the paper [5]. The algorithm in this paper can also be used in the applications where LPME plays a role.

State Space Realization Theorems For Data Mining

In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and tools of Hopf algebras.