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Toeplitz matrices commuting with tridiagonal matrices. (English) Zbl 0477.15005

##### MSC:
 15A18 Eigenvalues, singular values, and eigenvectors 15A27 Commutativity of matrices
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##### References:
 [1] F.A. Grünbaum, Eigenvectors of a Toeplitz matrix: discrete version of the prolate spheroidal wave functions, SIAM J. Alg. Discrete Meth., to appear. [2] Slepian, D.; Pollak, H.O., Prolate spheroidal wave functions, Fourier analysis and uncertainty I, Bell system tech. J., 40, 1, 43-64, (1961) · Zbl 0184.08601 [3] Landau, H.J.; Pollak, H.O., Prolate spheroidal wave functions, Fourier analysis and uncertainty II, Bell system tech. J., 40, 1, 65-84, (1961) · Zbl 0184.08602 [4] Landau, H.J.; Pollak, H.O., Prolate spheroidal wave functions, Fourier analysis and uncertainty III, Bell system tech. J., 41, 4, 1295-1336, (1962) · Zbl 0184.08603 [5] Slepian, D., Prolate spheroidal wave functions, Fourier analysis and uncertainty IV, Bell system tech. J., 43, 6, 3009-3058, (1964) · Zbl 0184.08604 [6] Slepian, D., Prolate spheroidal wave functions, Fourier analysis and uncertainty V, Bell system tech. J., 57, 5, 1371-1430, (1978) · Zbl 0378.33006 [7] Kailath, T., Inverses of Toeplitz operators, innovations and orthogonal polynomials, SIAM rev., 20, 1, 106-119, (1978) · Zbl 0382.47013 [8] Grünbaum, F.A., Second order differential operators commuting with convolution integral operators, LBL report 9298, (1979) [9] Gustavson, F.; Yun, D., Fast computation for Toeplitz systems, Cauchy-Hermite-pade approximants, and the extended Euclidean algorithm, IBM rc 7551, (Mar. 1979) [10] R. Brent, F. Gustavson, and D. Yun, Fast computation of Pade approximants and the solution of Toeplitz systems of equations, to appear. · Zbl 0475.65018 [11] Morrison, J., On the commutation of finite integral operators with difference kernels, and linear selfadjoint differential operators, abstract, Notices amer. math. soc., 119, (1962) [12] Widom, H., Asymptotic behavior of eigenvalues of certain integral equations II, Arch. rational mech. anal., 17, 215-229, (1964) · Zbl 0183.11701 [13] Wilkinson, J.; Reinsch, C., Handbook for automatic computation, vol. 2: linear algebra, (1971), Springer Berlin [14] Parlett, B., The symmetric eigenvalue problem, (1980), Prentice-Hall Englewood Cliffs, N.J · Zbl 0431.65017 [15] Magnus, W.; Oberhettinger, F.; Soni, R., Formulas and theorems for the special functions of mathematical physics, (1966), Springer · Zbl 0143.08502
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