A Contribution to the Feasibility of the Interval Gaussian Algorithm
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Alefeld, G. : On the Convergence of Some Interval-Arithmetic Modifications of Newton's Method, SIAM J. Numer. Anal. 21 (1984), pp. 363–372.
Alefeld, G.: Über die Durchführbarkeit des Gaußschen Algorithmus bei Gleichungen mil Intervallen als Koeffizienten, Computing Suppl. 1 (1977), pp. 15–19.
Alefeld, G. and Herzberger, J.: Einführung in die Intervallrechnung, Reihe Informatik 12, Bibliographisches Institut, Mannheim, 1974.
Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.
Alefeld, G. and Mayer, G.: The Gaussian Algorithm for Linear Systems with Interval Data, in: Carlson, D., Johnson, C. R., Lay, D. C., and Porter, A. D. (eds), Linear Algebra Gems: Assets for the Undergraduate Mathematics, The Mathematical Association of America, MAA Notes 59.
Barth, W. and Nuding, E: Optimale Lösung von Intervallgleichungssystemen, Computing 12 (1974), pp. 117–125.
Berman, A. and Plemmons, R. J.: Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics 9, SIAM, Philadelphia, 1994.
Frommer, A: A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure, in: Alefeld, G., Rohn, J., Rump, S., and Yamamoto, T. (eds), Symbolic Algebraic Methods and Verification Methods, SpringerMathematics, Springer, Wien, 2001, pp. 79–86.
Frommer, A. and Mayer, G.: A New Criterion to Guarantee the Feasibility of the Interval Gaussian Algorithm, SIAM J. Matrix Anal. Appl. 14 (1993), pp. 408–419.
Frommer, A. and Mayer, G.: Linear Systems with Ω-Diagonally Dominant Matrices and Related Ones, Linear Algebra Appl. 186 (1993), pp. 165–181.
Garloff, J.: Block Methods for the Solution of Linear Interval Equations, SIAM J. Matrix Anal. Appl. 11 (1990), pp. 89–106.
Hansen, E. R.: Gaussian Elimination in Interval Systems, preprint, 1997.
Hansen, E. R.: The Hull of Preconditioned Interval Linear Equations, Reliable Computing 6 (2) (2000), pp. 95–103.
Hansen, E. R. and Smith, R.: Interval Arithmetic in Matrix Computations, Part II, SIAM J. Numer. Anal. 4 (1967), pp. 1–9.
Hebgen, M.: Eine scaling-invariante Pivotsuche für Intervallmatrizen, Computing 12 (1974), pp. 99–106.
Klatte, R., Kulisch, U., Neaga, M., Ratz, D., and Ullrich, C.: PASCAL-XSC, Sprachbeschreibung mil Beispielen, Springer, Berlin, 1991.
Mayer, G.: Old and New Aspects of the Interval Gaussian Algorithm, in: Kaucher, E., Markov, S. M., and Mayer, G. (eds), Computer Arithmetic, Scientific Computation and Mathematical Modelling, IMACS Annals on Computing and Applied Mathematics 12, Baltzer, Basel, 1991, pp. 329–349.
Mayer, G. and Pieper, L.: A Necessary and Sufficient Criterion to Guarantee the Feasibility of the Interval Gaussian Algorithm for a Class of Matrices, Appl. Math. 38 (1993), pp. 205–220.
Mayer, G. and Rohn, J.: On the Applicability of the Interval Gaussian Algorithm, Reliable Computing 4 (3) (1998), pp. 205–222.
Mayer, J.: An Approach to Overcome Division by Zero in the Interval Gaussian Algorithm, Reliable Computing 8 (3) (2002), pp. 229–237.
Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.
Moré, J. J.: Nonlinear Generalizations of Matrix Diagonal Dominance with Applications to Gauss-Seidel Iterations, SIAM J. Numer. Anal. 9 (1972), pp. 357–378.
Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.
Neumaier, A.: New Techniques for the Analysis of Linear Interval Equations, Linear Algebra Appl. 58 (1984), pp. 273–325.
Nickel, K.: Interval-Analysis, in: Jacobs, D. A. H. (ed.), The State of the Art in Numerical Analysis, Academic Press, London, 1977, pp. 193–225.
Reichmann, K.: Ein hinreichendes Kriterium für die Durchführbarkeit des Intervall-Gauß-Algorithmus bei Intervall-Hessenberg-Matrizen ohne Pivotsuche, Z. Angew. Math. Mech. 59 (1979), pp. 373–379.
Rohn, J.: On Overestimations Produced by the Interval Gaussian Algorithm, Reliable Computing 3 (4) (1997), pp. 363–368.
Rump, S. M.: INTLAB—INTerval LABoratory, in: Csendes, T. (ed.), Developements in Reliable Computing, Kluwer Academic Publishers, Dordrecht, 1999, pp. 77–104.
Schäfer, U.: The Feasibility of the Interval Gaussian Algorithm for Arrowhead Matrices, Reliable Computing 7 (1) (2001), pp. 59–62.
Schätzle, F.: Überschätzung beim Gauss-Algorithmus für lineare Intervallgleichungssysteme, Diplomarbeit, Freiburger Intervall-Berichte 84/3 (1984), pp. 1–122.
Schwandt, H.: An Interval Arithmetic Approach for the Construction of an Almost Globally Convergent Method for the Solution of Nonlinear Poisson Equation on the Unit Square, SIAM J. Set. Statist. Comput. 5 (1984), pp. 427–452.