Accurate Bidiagonal Decomposition and Computations with Generalized Pascal Matrices

TL;DR

This paper introduces a precise method for bidiagonal factorization of generalized Pascal matrices, enabling accurate computation of their eigenvalues, singular values, and inverses, supported by numerical examples.

Contribution

It presents a novel accurate bidiagonal decomposition technique for generalized Pascal matrices, improving computational stability and precision.

Findings

High relative accuracy in eigenvalue computation

Effective bidiagonal factorization method demonstrated

Numerical examples validate the approach

Abstract

This paper provides an accurate method to obtain the bidiagonal factorization of many generalized Pascal matrices, which in turn can be used to compute with high relative accuracy the eigenvalues, singular values and inverses of these matrices. Numerical examples are included.