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Optimal finite characterization of linear problems with inexact data. (English) Zbl 1080.15002

The author proves that one cannot improve the result by J. Rohn, saying that any interval matrix property can be established by checking \(2^{2n-1}\) vertex matrices.

MSC:

15A06 Linear equations (linear algebraic aspects)
65G30 Interval and finite arithmetic
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References:

[1] Baumann, M.: A Regularity Criterion for Interval Matrices, in: Garloff, J. et al. (eds.), Collection of Scientific Papers Honoring Prof. Dr. Karl Nickel on Occasion of his 60th Birthday, Part I, Freiburg University, Freiburg, 1984, pp. 45–50.
[2] Kreinovich, V., Lakeyev, A., Rohn, J., and Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations, Kluwer Academic Publishers, Dordrecht, 1998. · Zbl 0945.68077
[3] Rohn, J.: Finite Characterization of Some Linear Problems with Inexact Data, in: Abstracts of SCAN’2000/Interval’2000, Karlsruhe, Germany, September 19–22, 2000, p. 32.
[4] Rohn, J.: Inverse Interval Matrix, SIAM Journal on Numerical Analysis 30 (1993), pp. 864–870. · Zbl 0781.65021 · doi:10.1137/0730044
[5] Rohn, J.: Positive Definiteness and Stability of Interval Matrices, SIAM Journal on Matrix Algebra and Applications 15 (1994), pp. 175–184. · Zbl 0796.65065 · doi:10.1137/S0895479891219216
[6] Rohn, J.: Systems of Linear Interval Equations, Linear Algebra and Its Applications 126 (1989), pp. 39–78. · Zbl 0712.65029 · doi:10.1016/0024-3795(89)90004-9
[7] Tsatsomeros, M. and Li, L.: A Recursive Test for P-Matrices, BIT Numerical Mathematics 40 (2) (2000), pp. 404–408. · Zbl 0960.65049 · doi:10.1023/A:1022307527408
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