Abstract
Linear complementarity problems (LCP) model many important mathematical problems. Ferris and Pang (1997) gave an extensive documentation of complementarity problems in engineering and equilibrium modeling. Meanwhile, validation methods have been found for example by Alefeld et al. (1999) to give guaranteed bounds on the distance between the numerical solution and the exact solution of the LCP. But the question remains open, if and/or how one still gets those guaranteed bounds, when the input data itself are not known exactly. We do not only think of real numbers like \(\sqrt 2\) or 1/3 that cannot be represented exactly on a computer, but we also think of mathematical problems for which even the exact real input data are not known.
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References
Alefeld, G., Chen, X., Potra, F. (1999): Numerical validation of solutions of linear complementarity problems. Numer. Math. 83: 1–23
Beeck, H. (1972): Über Struktur und Abschützungen der Lösungsmenge von linearen Gleichungssystemen mit Intervallkoeffizienten. Computing 10: 231–244
Collatz, L. (1981): Differentialgleichungen. Teubner Studienbücher, Stuttgart
Cottle, R.W., Pang, J.S., Stone, R.E. (1992): The linear complementarity problem. Academic Press
Cryer, C.W., Lin, Y. (1985): An alternating direction implicit algorithm for the solution of linear complementarity problems arising from free boundary problems. Appl. Math. Optim. 13: 1–17
Ferris, M.C., Pang, J.S. (1997): Engineering and economic applications of complementarity problems. Siam Rev. Vol 39, No. 4: 669–713.
Gwinner, J. (1988): Acceptable solutions of linear complementarity problems. Computing 40: 361–366
Hansen, E. (1969): On solving two-point boundary-value problems using interval arithmetic. In: Hansen, E. (ed.): Topics in Interval Analysis. Clarendon Press, Oxford, pp. 74–90
Mayer, G. (1991): Old and new aspects for the interval Gaussian algorithm. In: Kaucher, E., Markov, S.M., Mayer, G. (eds.): Computer Arithmetic, Scientific Computation and Mathematical Modelling. J. C. Baltzer AG, Basel, pp. 329–349
Oettli, W., Prager W. (1964): Compatibility of approximate solutions of linear equations with given error bounds for coefficients and right-hand sides. Numer. Math. 6: 405–409
Schüfer, U. (1999): Das lineare Komplementaritütsproblem mit Intervalleintrügen. Thesis. Universitüt Karlsruhe
Thompson, R.C., Walter, W. (1992): An existence theorem for a parabolic free boundary problem. Differential and Integral Equations 5: 43–54
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Schäfer, U. (2001). The Linear Complementarity Problem with Interval Data. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_21
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DOI: https://doi.org/10.1007/978-3-7091-6280-4_21
Publisher Name: Springer, Vienna
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