Abstract
In this paper the numerical stability of the orthogonal factorization method [5] for linear equality-constrained quadratic programming problems is studied using a backward error analysis. A perturbation formula for the problem is analyzed; the condition numbers of this formula are examined in order to compare them with the condition numbers of the two matrices of the problem. A class of test problems is also considered in order to show experimentally the behaviour of the method.
Zusammenfassung
Mit Hilfe einer Rückwärtsanalyse untersuchen wir die numerische Stabilität der orthogonalen Faktorisierung nach [5] für quadratische Optimierungsprobleme mit linearen Gleichungsbedingungen. Dabei wird eine Störungsformel für das Problem analysiert, deren Konditionszahlen mit den Konditionszahlen der zwei Matrizen des Problems verglichen werden. Experimentell wird das Verhalten des Verfahrens mit Hilfe einer Klasse von Testproblemen untersucht.
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Work supported by M.U.R.S.T. 40% projectAnalisi Numerica e Matematica Computazionale.
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Galligani, E., Zanni, L. Error analysis of an algorithm for equality-constrained quadratic programming problems. Computing 58, 47–67 (1997). https://doi.org/10.1007/BF02684471
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DOI: https://doi.org/10.1007/BF02684471