Identification of induction curves

Levente Lócsi

Abstract


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 \(p\) be reconstructed given the induction curve, i.e. the case of \(2 \times 2\) matrices is examined. The analytic solution is not possible in most cases already in this planar setting, therefore numerical approximation methods shall be applied.

Keywords


matrix norms; power norm; \(p\)-norm; induction curves; identification; optimization; \(p\)-eigenvectors; Nelder--Mead method

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2023.3.01

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