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 
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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

[1] A. S. Householder: The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company 1965. | MR

[2] A. Ralston: A First Course in Numerical Analysis. Mc Graw-Hill Book Company, 1965. | MR | Zbl

[3] R. S. Vargа: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1962. | MR

[4] V. Jarník: Differential Calculus II. (in Czech). Nakladatelství ČSAV, Praha 1956.

[5] I. Marek: Iterations of Linear Bounded Operators in Non Self-Adjoint Eigenvalue Problems and Kellogg's Iteration Process. Czech. Math. Journal, 12 (87), 536-554, Prague. | Zbl

[6] O. D. Kellogg: On the existence and closure of sets of characteristic functions. Math. Annalen, Band 86, Berlin 1922.

[7] F. Riesz B. Nagy: Lecons d'analyse fonctionelle. Budapest 1953.

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