High Relative Accuracy With Collocation Matrices of q$$ q $$‐Jacobi Polynomials

ABSTRACT Little ‐Jacobi polynomials belong to the field of quantum calculus. This article obtains the bidiagonal decomposition of the collocation matrices of these polynomials, showing that, in many cases, it can be constructed to high relative accuracy (HRA). Then, it can be used to compute with HRA the inverses, eigenvalues, and singular values of these matrices. Numerical experiments are provided and illustrate the excellent results obtained when applying the presented methods.