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Recursive inversion of Hankel matrices. (English) Zbl 0684.65020

Orthogonal polynomials and their applications, 2nd Int. Symp., Segovia/Spain 1986, Monogr. Acad. Cienc. Exactas, Fís., Quím., Nat., Zaragoza, 119-128 (1988).
[For the entire collection see Zbl 0667.00014.]
This paper presented a recursive algorithm for the inversion of an arbitrary invertible Hankel matrix. The connections between the algorithm and the formal orthogonal polynomials and the reproducing kernels for non-definite linear functionals are discussed. Applications of the algorithm to the study of problems on formal orthogonal polynomials such as Padé approximates and the \(\epsilon\)-algorithm are also given.
It will be of interest to note that Hankel matrices generated by the Markov parameters of a linear time invariant system have applications in the system realization problems. Thus, the algorithm presented in this paper may also find some interesting applications in system theory.
Reviewer: Wu Minyen

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
15A09 Theory of matrix inversion and generalized inverses
65K10 Numerical optimization and variational techniques

Citations:

Zbl 0667.00014