In this paper, stability properties of 2×2 hypermatrices of the form
are investigated, where ε is a small parameter. Stability theorems on these and similar matrices play an important role in the convergence analysis of certain numerical methods of mathematical programming and control theory, as pointed out in Refs. 1–3.
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Gerencsér, L.,On the Use of Stability Theory in the Design of Algorithms for Structured Nonlinear Optimization Problems, Problems of Control and Information Theory, Vol. 7, pp. 471–482, 1978.
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The author is indebted to Mrs. K. Hangos and Miss M. Kovács for the careful reading of the manuscript.
Communicated by R. E. Kalaba
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Gerencsér, L. Stability theorems for 2×2 hypermatrices. J Optim Theory Appl 35, 1–7 (1981). https://doi.org/10.1007/BF00934699
- Mathematical programming
- control theory
- numerical methods
- convergence theorems
- stability theorems
- discrete-time dynamical systems