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

T. Bella, V. Olshevsky, P. Zhlobich

Research output: Contribution to journalArticlepeer-review

Abstract

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. (C) 2009 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)2032-2051
Number of pages20
JournalLinear algebra and its applications
Volume432
Issue number8
DOIs
Publication statusPublished - 1 Apr 2010

Keywords

  • Quasiseparable matrix
  • Signal flow graphs
  • Digital filter structures
  • Horner and Clenshaw rules
  • Polynomial-Vandermonde matrices
  • Fast algorithms
  • VANDERMONDE MATRICES
  • POLYNOMIALS
  • SCATTERING
  • ALGORITHM

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