Abstract
The generalized Lanczos process applied to a normal matrix A builds up a condensed form of A, which can be described as a band matrix with slowly growing bandwidth. For certain classes of normal matrices, the bandwidth turns out to be constant. It is shown that, in such cases, the bandwidth is determined by the degree of the minimal polyanalytic polynomial of A. It was in relation to the generalized Lanczos process thatM.Huhtanen introduced the concept of the minimal polyanalytic polynomial of a normal matrix.
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References
Yu. Saad, Iterative Methods for Sparse Linear Systems (SIAM, Philadelphia, 2003; Izd. Moskov. Univ., Moscow, 2013).
M. Huhtanen, “Orthogonal polyanalytic polynomials and normal matrices,” Math. Comp. 72 (241), 355–373 (2002).
L. Elsner and Kh. D. Ikramov, “On a condensed form for normal matrices under finite sequences of elementary unitary similarities,” Linear Algebra Appl. 254, 79–98 (1997).
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Original Russian Text © Kh.D. Ikramov, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 1, pp. 56–61.
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Ikramov, K.D. Solving Systems of Linear Equations with Normal Coefficient Matrices and the Degree of the Minimal Polyanalytic Polynomial. Math Notes 104, 48–52 (2018). https://doi.org/10.1134/S0001434618070064
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DOI: https://doi.org/10.1134/S0001434618070064