High Relative Accuracy With Collocation Matrices of q$$ q $$‐Jacobi Polynomials
Copyright policy )High Relative Accuracy With Collocation Matrices of q$$ q $$‐Jacobi Polynomials
ABSTRACTLittle ‐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.
- University of Zaragoza Spain
Numerical computation of eigenvalues and eigenvectors of matrices, little \(q\)-Legendre polynomials, \(q\)-integers, Direct numerical methods for linear systems and matrix inversion, quantum calculus, 510, 620, bidiagonal decomposition, little \(q\)-Jacobi polynomials, quantum orthogonal polynomials, total positivity, high relative accuracy
Numerical computation of eigenvalues and eigenvectors of matrices, little \(q\)-Legendre polynomials, \(q\)-integers, Direct numerical methods for linear systems and matrix inversion, quantum calculus, 510, 620, bidiagonal decomposition, little \(q\)-Jacobi polynomials, quantum orthogonal polynomials, total positivity, high relative accuracy
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