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Authors: LEVENTE LÓCSI.
Received 01 March 2023; Accepted 14 August 2023. Published Online: 2023-09-30
Published Print: 2023-09-30
pp. 467-480
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Induction curves (induction surfaces, induction sets in general) were recently introduced to provide a visual aid to examine the fractions defining the norm of a matrix, along with the discovery and description of p-eigenvectors. In our current investigation we delve into an inverse problem, the identification of induction curves. Namely: could the elements of the matrix and the used power parameter pbe reconstructed given the induction curve, i.e. the case of 2 x 2 matrices is examined. The analytic solution is not possible in most cases already in this planar setting, therefore numerical approximation methods shall be applied.
Mathematics Subject Classification (2010): 15A83, 47A30, 65F20, 65F35.
Keywords: Matrix norms, power norm, p-norm, induction curves, identification, optimization, p-eigenvectors, Nelder-Mead method.
