Inverse and factorization of triangular Toeplitz matrices

Abstract

In this paper, we present a new approach for finding the inverse of some triangular Toeplitz matrices using the generalized Fibonacci polynomials and give a factorization of these matrices. We also give a new proof of Trudi's formula using our result.

Rayleigh anomaly induced phase gradients in finite nanoparticle chains

“…According to the above derivation, to solve for p we need to solve two systems with triangular Toeplitz matrices, each has an analytical solution for the required matrix inversion. 38,54 The inverse of is also a finite lower/upper triangular Toeplitz matrix: 54 where B q = B | i − j | ( q = | i − j |) can be found based on the generalized Fibonacci polynomials: 54 …”

General approach to function approximation

“…To invert the matrix a recursive formula based on generalized Fibonacci polynomials is available [24]. The a n coefficients in (19) are expressed in terms of g n and f n as follows…”