Geodesic
Kellogg's iterations for general complex matrix
Applications of Mathematics, Tome 19 (1974) no. 5, pp. 342-365

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Let $A$ be a nonzero complex matrix $n \times n, x_0\in V_n(C), x_0\neq\Theta$. Let us define $x_k=A^kx_0$, $\mu_k=x^H_kx_k/x^H_{k-1}x_{k-1}$ and $v_k=x^H_{k-1}x_k/x^H_{k-1}x_{k-1}$. In this paper, assymptotic behaviour of the numbers $\mu_k$ and $v_k$ is studied in detail, mainly for matrices with nonlinear elementary divisors.
Let $A$ be a nonzero complex matrix $n \times n, x_0\in V_n(C), x_0\neq\Theta$. Let us define $x_k=A^kx_0$, $\mu_k=x^H_kx_k/x^H_{k-1}x_{k-1}$ and $v_k=x^H_{k-1}x_k/x^H_{k-1}x_{k-1}$. In this paper, assymptotic behaviour of the numbers $\mu_k$ and $v_k$ is studied in detail, mainly for matrices with nonlinear elementary divisors.
DOI : 10.21136/AM.1974.103550
Classification : 15A18, 65B05, 65F15 
Zítko, Jan. Kellogg's iterations for general complex matrix. Applications of Mathematics, Tome 19 (1974) no. 5, pp. 342-365. doi: 10.21136/AM.1974.103550
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