Signal flow graph approach to inversion of (H,m)-quasiseparable-Vandermonde matrices and new filter structures

We use the language of signal flow graph representation of digital filter structures to solve three purely mathematical problems, including fast inversion of certain polynomial-Vandermonde matrices, deriving an analogue of the Horner and Clenshaw rules for polynomial evaluation in a (H,m)-quasiseparable basis, and computation of eigenvectors of (H,m)-quasiseparable classes of matrices. While algebraic derivations are possible, using elementary operations (specifically, flow reversal) on signal flow graphs provides a unified derivation, reveals connections with systems theory, etc.