Identification of induction curves
DOI:
https://doi.org/10.24193/subbmath.2023.3.01Keywords:
Matrix norms, power norm, p-norm, induction curves, identification, optimization, p-eigenvectors, Nelder–Mead method.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 × 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.
References
Argyros, I.K., George, S., Senapati, K., Extended local convergence for Newton-type solver under weak conditions, Stud. Univ. Babeș-Bolyai Math., 66(2021), no. 4, 757-768.
Bokor, J., Schipp, F., Approximate linear H∞ identification in Laguerre and Kautz basis, Automatica J. IFAC, 34(1998), 463-468.
Cadzow, J.A., Minimum l1, l2 and l∞ norm approximate solutions to an overdetermined system of linear equations, Digital Signal Processing, 12(2002), 524-560.
Chang, S., Li, C.K., Certain isometries on Rn, Linear Algebra Appl., 165(1992), 251-265.
Csirmaz, L., An optimization problem for continuous submodular functions, Stud. Univ. Babeș-Bolyai Math., 66(2021), no. 1, 211-222.
Fărcășeanu, M., Grecu, A., Mihăilescu, M., Stancu-Dumitru, D., Perturbed eigenvalue problems: An overview, Stud. Univ. Babeș-Bolyai Math., 66(2021), no. 1, 55-73.
Fridli, S., Lócsi, L., Schipp, F., Rational function systems in ECG processing, Proc. 13th Int. Conf. Computer Aided Systems Theory (EUROCAST), Part I, Springer LNCS 6927 (2011), 88-95.
Hegedűs, Cs., The method IRLS for some best lp norm solutions of under- or overdetermined linear systems, Ann. Univ. Sci. Budapest. Sect. Comput., 45(2016), 303-317.
Kovács, P., Lócsi, L., RAIT, the Rational Approximation and Interpolation Toolbox for Matlab, with experiments on ECG signals, Int. J. of Advances in Telecommunications, Electrotechnics, Signals and Systems (IJATES2), 1(2012), no. 2-3, 67-75.
Li, C.K., So, W., Isometries of fp norm, Amer. Math. Monthly, 101(1994), 452-453.
Lócsi, L., A hyperbolic variant of the Nelder-Mead simplex method in low dimensions, Acta Univ. Sapientiae Math., 5(2013), no. 2, 169-183.
Lócsi, L., Introducing p-eigenvectors, exact solutions for some simple matrices, Ann. Univ. Sci. Budapest. Sect. Comput., 49(2019), 325-345.
Lócsi, L., Németh, Zs., On the construction of p-eigenvectors, Ann. Univ. Sci. Budapest. Sect. Comput., 50(2020), 231-247.
Nelder, J.A., Mead, R., A simplex method for function minimization, Comput. J., 7(1965), 308-313.
Samia, K., Djamel, B., Hybrid conjugate gradient-BFGS methods based on Wolfe line search, Stud. Univ. Babeș-Bolyai Math., 67(2022), no. 4, 855-869.
Schipp, F., On Lp-norm convergence of series with respect to product systems, Anal. Math., 2(1976), 49-64.
Vinh, N.T., Thuong, N.T., A relaxed version of the gradient projection method for variational inequalities with applications, Stud. Univ. Babeș-Bolyai Math., 67(2022), no. 1, 73-89.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
