Accurate Computations with Generalized Pascal k -Eliminated Functional Matrices

Jorge Delgado, Héctor Orera () and Juan Manuel Peña
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Jorge Delgado: Departamento de Matemática Aplicada, Universidad de Zaragoza, 50018 Zaragoza, Spain
Héctor Orera: Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain
Juan Manuel Peña: Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain

Mathematics, 2025, vol. 13, issue 2, 1-14

Abstract: This paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal k -eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally positive or inverse of totally positive matrices are provided. In these cases, the presented method can be used to compute their eigenvalues, singular values and inverses with high relative accuracy. Numerical examples illustrate the high accuracy of our approach.

Keywords: bidiagonal decomposition; high relative accuracy; total positivity; k-eliminated Pascal matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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