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Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle. (English) Zbl 0777.65013

It is shown that the Levinson algorithm for the inverse Cholesky factorization of positive definite Toeplitz matrices is a special case of a more general method. An efficient implementation of the Arnoldi process for isometric operators is given. A Gaussian quadrature on the unit circle is derived.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
30E10 Approximation in the complex plane
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
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