A nonlinear generalization of the Filbert matrix and its Lucas analogue

Abstract

In this paper, we present both a new generalization and an analogue of the Filbert matrix by the means of the Fibonacci and Lucas numbers whose indices are in nonlinear form for the positive integers and the integers r, s, c. This will be the first example as nonlinear generalizations of the Filbert and Lilbert matrices. Furthermore, we present q-versions of these matrices and their related results. We derive explicit formulæ for the inverse matrix, the LU-decomposition and the inverse matrices , as well as we present the Cholesky decomposition for all matrices.

Keywords:

• Filbert matrix
• LU-decomposition
• inverse matrix
• backward induction
• Cholesky decomposition
• generalized q-Pochhammer notation

AMS Subject Classifications:

• 15A09
• 15A23
• 11B39
• 15B36
• 05A30

Notes

No potential conflict of interest was reported by the authors.