Институт вычислительной математики
и математической геофизики

Abstracts

Computational algebra

The fundamental polynomials $q_k(x)$ of the symmetric Toeplitz matrix $G_k$, $k=0(1)n$, are connected with the fundamental polynomials of persymmetric Hankel matrix ${ ilde H}_k$, ${ ilde H}_k=G_kJ_k$, where $J_k$ is the contridentity matrix of the order of $k$. It is shown that the relations eqs{ q_k(x)=xq_{k-1}(x)+q_k(0){ar q}_{k-1}(x), {ar q}_k(x)=xq_{k-1}(x)+(-1)^k{ar q}_{k-1}(x), {ar q}_{k-1}(x)=x^{k-1}q_{k-1}(1/x) } are the corollary of this connections.

Note. Abstracts are published in author's edition

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