Symbolic computation for operators with matrix coefficients
Sprache des Vortragstitels:
Foundations of Computational Mathematics (FoCM) 2017
Sprache des Tagungstitel:
In order to facilitate symbolic computations with systems of linear functional equations an algebraic framework for such systems is needed for effective computations in corresponding rings of operators. Normal forms of operators are a key ingredient for that.
We generalize the recently developed tensor approach from scalar equations to the matrix case, by allowing noncommutative coefficients. The tensor approach is flexible enough to cover many operators, like integral operators, that do not fit the well-established framework of skew-polynomials. Noncommutative coefficients even allow to handle systems of generic size. Normal forms rely on a confluent reduction system.
Based on our implementation of tensor reduction systems, we implemented the ring of integro-differential operators with time-delay and we worked out normal forms for those operators. We use this to partly automatize certain computations related to differential time-delay systems, e.g. Artstein's reduction of differential time-delay control systems.