Piñar, M. A.; Ramírez, V. 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 Cited in 2 Documents 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 Keywords:inversion of Hankel matrices; epsilon-algorithm; recursive algorithm; formal orthogonal polynomials; reproducing kernels; Padé approximates; Markov parameters; linear time invariant system; time-invariant Citations:Zbl 0667.00014 PDFBibTeX XML