Abstract
The constants defining a system of linear equations may be subject to incertainties. In this case the induced variations of the solution can be effectively bounded by methods of interval analysis. In the worst case the complexity of this problem is exponential in the number of variables. We consider Rohn's sign-accord algorithm to solve the problem. A parallel version of the method is developed using rounded interval arithmetic. Theoretical considerations as well as numerical tests indicate that the parallelling is efficient (i.e. the speedup is near linear) if an appropriate number of parallel processors is allocated. This number can be estimated before the start of the parallel process.
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References
Akl, S.G. (1982). The Design and Analysis of Parallel Algorithms. Prentice Hall.
Baumann, M. (1983). Řesenà Soustav Intervalových LineárÃch Rovnic. Master's Thesis. Charles University, Prague.
Henriksen, T. & Toft, O. (1992). C++ Interval, Matrix, and Interval Matrix Libraries. Report NI-92-08, Institute for Numerical Analysis, The Technical University of Denmark.
Madsen, K. & Toft, O. (1994). A Parallel Method for Linear Interval Equations. To appear in Interval Computations.
Neumaier, A. (1990). Interval Methods for Systems of Equations. Cambridge University Press.
Oettli, W. & Prager, W. (1964). Compatibility of Approximate Solution of Linear Equations with Given Error Bounds for Coefficients and Right-hand sides. Numer. Math. 6:405–409.
Rohn, J. (1989). Systems of Linear Interval Equations. Linear Algebra Appl., 126:39–78.
Toft, O. (1992). Sequential and Parallel Solution of Linear Interval Equations. Master's Thesis. Institute for Numerical Analysis, The Technical University of Denmark.
Vorst, H.A. and Dooren, P., eds. (1990). Parallel Algorithms for Numerical Linear Algebra. North Holland, Amsterdam.
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© 1994 Springer-Verlag Berlin Heidelberg
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Madsen, K., Toft, O. (1994). Parallel interval methods for perturbed linear systems. In: Dongarra, J., Waśniewski, J. (eds) Parallel Scientific Computing. PARA 1994. Lecture Notes in Computer Science, vol 879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030164
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DOI: https://doi.org/10.1007/BFb0030164
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