An inverse problem for Toeplitz matrices and the synthesis of discrete transmission lines

Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review

Abstract

Let Am be a positive definite, m x m, Toeplitz matrix. Let Ak be its k x k principal minor (for any k≤m), which is also positive definite and Toeplitz. Define the central mass sequence {ρ{variant}1,...,ρ{variant}m} by ρ{variant}k = sup{ρ{variant}: Ak - ρ{variant}Πk > 0}, in which Πk is the k x k matrix of all 1's. We show how knowledge of the sequence {ρ{variant}k} is equivalent to knowledge of the matrix Am. This result has application to the direct and inverse problems for a transmission line which consists of piecewise constant components. Knowing the impulse response of the transmission line, we can calculate the capacitance taper of the line, and vice versa.

Original languageEnglish (US)
Pages (from-to)207-225
Number of pages19
JournalLinear Algebra and Its Applications
Volume38
Issue numberC
DOIs
StatePublished - Jun 1981

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'An inverse problem for Toeplitz matrices and the synthesis of discrete transmission lines'. Together they form a unique fingerprint.

Cite this