A right-preconditioning process for the formal-algebraic approach to inner and outer estimation of AE-solution sets

Reliable Computing

Volumn 11, Issue 6, 2005, Pages 443-478

  Goldsztejn, Alexandre ^a,b  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b THALES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; SET THEORY; VECTORS;

AE-SOLUTION SETS; HIGH DIMENSION PROBLEMS; LINEAR INTERVAL SYSTEMS; RIGHT-PRECONDITIONING PROCESS;

LINEAR SYSTEMS;

EID: 23844516114     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11155-005-0404-x     Document Type: Article

References (20)

1. Beaumont, O.: Algorithmique pour les Intervalles, Ph.D. Thesis, Université de Rennes 1, 1999.
2. Beaumont, O.: Solving Interval Linear Systems with Oblique Boxes, Publication interne IRISA, 2000, http://www.irisa.fr/sage/publications/Category/RR.html.
3. Dimitrova.N. S.,Markov, S. M., and Popova.E.D.: Extended Interval Aritrhmetics: New Results and Applications, in: Computer Arithmetics and Enclosure Methods, 1992, pp. 225-232.
4. Eijgenraam, P.: The Solution of Initial Value Problems Using Interval Arithmetic, Mathematical Centre Tracts 144, Stichting Mathematisch Centrum, Amsterdam, 1981.
5. Kaucher, E.: Interval Analysis in the Extended Interval Space, Computing, Suppl. 2 (1980), pp. 33-49.
6. Kaucher, E.: Uber metrische und algebraische Eigenschaften einiger beim numerischen Rechnen auftretender Raume, Ph.D. Thesis, Karlsruhe, 1973.
7. Lohner, R. J.: Enclosing the Solutions of Ordinary Initial and Boundary Value Problems, in: Computer Arithmetic: Scientific Computation and Programming Languages, Wiley-Teubner Series in Computer Science, Stuttgart, 1987, pp. 255-286.
8. Markov, S. M., Popova, E. D., and Ullrich, Ch.: On the Solution of Linear Algebraic Equations Involving Interval Coefficients, Iterative Methods in Linear Algebra, IMACS Series on Computational and Applied Mathematics 3 (1996), pp. 216-225.
9. Mayer, G. and Warnke, L: On the Fixed Points of the Interval Function f([x]) = [a][x] + [b], Linear Algebra and Its Applications 363 (2003), pp. 201-216.
10. Neumaier, A.: Interval Methods for Systems of Equations, Cambridge Univ. Press, Cambridge, 1990.
11. Neumaier, A.: On Shary's Algebraic Approach for Linear Interval Equations, SIAM J. Matrix Anal. Appl. 21 (2000), pp. 1156-1162.
12. Neumaier, A.: Overestimation in Linear Interval Equations, SIAM J. Numer. Anal. 24 (1) (1987), pp. 207-214.
13. Popova, E. D.: Multiplication Distributivity of Proper and Improper Intervals, Reliable Computing 7 (2) (2001), pp. 129-140.
14. Sainz, M. Á., Gardeñes, E., and Jorba, L.: Formal Solution to Systems of Interval Linear or Non-Linear Equations, Reliable Computing 8 (3) (2002), pp. 189-211.
15. Sainz, M. Á., Gardeñes, E., and Jorba, L.: Interval Estimations of Solutions Sets to Real-Valued Systems of Linear or Non-Linear Equations, Reliable Computing 8 (4) (2002), pp. 283-305.
16. Shary, S. P.: A New Technique in Systems Analysis under Interval Uncertainty and Ambiguity, Reliable Computing 8 (5) (2002), pp. 321-418.
17. Shary, S. P.: Algebraic Approach in the "Outer Problem" for Interval Linear Equations, Reliable Computing 3 (2) (1997), pp. 103-135.
18. Shary, S. P.: Algebraic Approach to the Interval Linear Static Identification, Tolerance and Control Problems, or One More Application of Kaucher Arithmetic, Reliable Computing 2 (1) (1996), pp. 3-33.
19. Shary, S. P.: Outer Estimation of Generalized Solution Sets to Interval Linear Systems, Reliable Computing 5 (3) (1999), pp. 323-335.
20. SIGLA/X group: Modal Intervals, Reliable Computing 7 (2) (2001), pp. 77-111.