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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J\sb 0(z)- iJ\sb 1(z)$ and of Bessel functions $J\sb m(z)$ of any real order $m$. (English) Zbl 0805.65037
Eigenvalues of an infinite complex symmetric matrix are computed as limits of the eigenvalues of its leading submatrices. Convergence properties of this sequence are investigated, and the computation of the zeros of a combination of Bessel functions is used as a numerical example.

65F15Eigenvalues, eigenvectors (numerical linear algebra)
65D20Computation of special functions, construction of tables
65H05Single nonlinear equations (numerical methods)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
Full Text: DOI
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