Structure theory and fast inversion of Hankel striped matrices. I (Q922616)

Hankel striped matrices are matrices of the form \(H=[H_ 1H_ 2...H_ r]\) where the \(H_ j\) are \(m\times n_ j\) Hankel matrices. A structure theory is developed for the kernel of a Hankel striped matrix. This theory is based on the consideration of the family of Hankel striped matrices \(H^{(k)}=[H_ 1^{(k)}H_ 2^{(k)}...H_ r^{(k)}]\) where \(H_ j^{(k)}\) is the \(k\times (m+n_ j-k)\) Hankel matrix determined by \(H_ j\). In particular, the partial indices (in the sense of another paper by the author [ibid. 8, 805-824 (1985; Zbl 0595.47015)]) are identified. Using this structure theory, fast algorithms are developed for inversion of Hankel striped matrices. The well-known Levinson-Trench algorithm appears as a very special case of these fast algorithms.