Enclosing solutions of linear equations

SIAM Journal on Numerical Analysis

Volumn 35, Issue 2, 1998, Pages 524-539

  Rohn, Jiri ^a,b   Rex, Georg ^c  

^a CHARLES UNIVERSITY   (Czech Republic)

^b INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

^c UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Enclosure; Finite termination; Interval free; Linear equations

Indexed keywords

EID: 0347669506     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996299423     Document Type: Article

References (16)

1. G. ALEFELD AND J. HERZBERGER, Introduction to Interval Computations, Academic Press, New York, 1983.
2. R. HAMMER, M. HOCKS, U. KULISCH, AND D. RATZ, Numerical Toolbox for Verified Computing I, Springer-Verlag, Berlin, 1993.
3. R. KRAWCZYK, Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing. 4 (1969), pp. 187-201.
4. R. KRAWCZYK, Intervalliterationsverfahren, Bericht 186, Mathematisch-Statistische Sektion im Forschungszentrum Graz, Graz, Austria, 1982.
5. R. E. MOORE, A test for existence of solutions to nonlinear systems, SIAM J. Numer. Anal., 14 (1977), pp. 611-615.
6. A. NEUMAIER, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, UK, 1990.
7. H.-G. REX, Zur Lösungseinschließung linearer Gleichungssysteme, Wiss. Z. Tech. Hochschule Leipzig, 15 (1991), pp. 441-447.
8. G. REX, Zu a posteriori Fehlerabschätzungen bei linearen Gleichungssystemen, Z. Angew. Math. Mech., 72 (1992), pp. T640-T643.
9. G. REX, Parameterabhängige Lösungseinschließungen linearer Gleichungssysteme, Z. Angew. Math. Mech., 74 (1994), pp. T683-T685.
10. J. ROHN, Validated Solutions of Linear Equations, Tech. report 620, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, January 1995.
11. S. M. RUMP, Solving algebraic problems with high accuracy, in A New Approach to Scientific Computation, U. Kulisch and W. Miranker, eds., Academic Press, New York, 1983, pp. 51-120.
12. S. M. RUMP, Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds, Computing Suppl., 5 (1984), pp. 147-168.
13. S. M. RUMP, New results on verified inclusions, in Accurate Scientific Computations, W. L. Miranker and R. A. Toupin, eds., Lecture Notes in Computer Science 235, Springer-Verlag, Berlin, 1986, pp. 31-69.
14. S. M. RUMP, On the solution of interval linear systems, Computing, 47 (1992), pp. 337-353.
15. S. M. RUMP, Verification methods for dense and sparse systems of equations, in Topics in Validated Computations, J. Herzberger, ed., North-Holland, Amsterdam, 1994, pp. 63-135.
16. R. VARGA, Matrix Iterative Analysis, Prentice-Hall. Englewood Cliffs, NJ, 1962.