Introduction to NonA

• The algebraic formulations of the parameter estimation problem for signals defined by ordinary differential equations with possibly polynomial coefficients (e.g., exponentials, sinusoidals, orthogonal polynomials such as Chebyshev, Jacobi, Legendre, Laguerre, Hermite, etc., Taylor expansions, Fourier expansions, expansions in an orthogonal basis defined by a family of orthogonal polynomials).
• The computation of annihilators for polynomials with parameters, namely, ordinary differential operators with polynomial coefficients in the Laplace variable s which annihilate the polynomial.
• The computation of annihilators which contain only certain given parameters by means of elimination techniques, i.e., by means of Gröbner basis techniques over noncommutative rings of ordinary differential operators with polynomial coefficients (e.g., Weyl algebras and polynomial extensions of the Weyl algebras (Stafford 1978, Quadrat & Robertz 2007, Quadrat & Robertz 2014)).
• The computation of annihilators which annihilate a given polynomial but not another one.