A Nonlinear Filbert-Like Matrix With Three Free Parameters: From Linearity To Nonlinearity

Abstract

Filbert and Lilbert matrices are defined by terms of linear Fibonacci-like sequences. By considering terms of such linear recurrences and additional free parameters, we define a nonlinear variant of these matrices via ratios of q-forms of terms of Fibonacci-like sequences whose indices are in nonlinear forms. We derive explicit formulae for the matrices L and U come from LU-decomposition, their inverses, inverse of the main matrices and their determinants.