Bidiagonal Factorizations of Filbert and Lilbert Matrices
Yasmina Khiar,
Esmeralda Mainar,
Juan Manuel Peña,
Eduardo Royo-Amondarain,
Beatriz Rubio
Affiliations
Yasmina Khiar
Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50009 Zaragoza, Spain
Esmeralda Mainar
Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50009 Zaragoza, Spain
Juan Manuel Peña
Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50009 Zaragoza, Spain
Eduardo Royo-Amondarain
Department of Mathematics, Centro de Astropartículas y Física de Altas Energías (CAPA), University of Zaragoza, 50009 Zaragoza, Spain
Beatriz Rubio
Department of Applied Mathematics, University Research Institute of Mathematics and Its Applications (IUMA), University of Zaragoza, 50009 Zaragoza, Spain
Extensions of Filbert and Lilbert matrices are addressed in this work. They are reciprocal Hankel matrices based on Fibonacci and Lucas numbers, respectively, and both are related to Hilbert matrices. The Neville elimination is applied to provide explicit expressions for their bidiagonal factorization. As a byproduct, formulae for the determinants of these matrices are obtained. Finally, numerical experiments show that several algebraic problems involving these matrices can be solved with outstanding accuracy, in contrast with traditional approaches.
