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Accurate computations with Wronskian matrices of Bessel and Laguerre polynomials. (English) Zbl 1493.15054

The authors provide an accurate method to obtain the bidiagonal factorization of some Wronskian matrices of Bessel polynomials and Laguerre polynomials. These Wronskian matrices are nonsingular and totally positive so that their bidiagonal factorizations do exist. This method can be used to compute their singular values and their inverses with high relative accuracy. Using standard symbolic computation software some numerical examples are given to illustrate the theoretical results.
Reviewer: Tin Yau Tam (Reno)

MSC:

15A23 Factorization of matrices
15A18 Eigenvalues, singular values, and eigenvectors
15A06 Linear equations (linear algebraic aspects)
15A09 Theory of matrix inversion and generalized inverses
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
65G50 Roundoff error
65F05 Direct numerical methods for linear systems and matrix inversion

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References:

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