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Gaussian Elimination
Linear System
Matrix Equation
Multiple Right Hand Sides
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Results concerning interval linear systems with multiple righthand sides and the interval matrix equation AX=B
Results concerning interval linear systems with multiple righthand sides and the interval matrix equation AX=B,10.1016/j.cam.2010.12.015,Journal of C
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Results concerning interval linear systems with multiple righthand sides and the interval matrix equation AX=B
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Citations: 1
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Behnam Hashemi
,
Mehdi Dehghan
This note tries to study different solution sets of the interval linear
matrix equation
AX=B, where A is a known square interval matrix of dimension m×m, B is a rectangular interval matrix of dimension m×n, while the unknown matrix X is also of dimension m×n. Firstly, we show that Shary’s results for interval linear systems with a single righthand side vector cannot be simply generalized to the case of interval linear systems of the form AX=B. Secondly, we give some analytical characterizations of the AEsolution sets of this interval matrix equation. We use a linear programming method in order to find the interval hull matrix. On the other hand, we propose the use of an interval
Gaussian elimination
to find an enclosure for the united solution set of this matrix equation, since the LU decomposition of A is needed only once. Numerical examples have also been given.
Journal:
Journal of Computational and Applied Mathematics  J COMPUT APPL MATH
, vol. 235, no. 9, pp. 29692978, 2011
DOI:
10.1016/j.cam.2010.12.015
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References
(11)
A BLOCK VERSION OF BICGSTAB FOR LINEAR SYSTEMS WITH MULTIPLE RIGHTHAND SIDES
(
Citations: 11
)
A. EL GUENNOUNI
,
K. JBILOU
,
H. SADOK
On the matrix equation AX=B with applications to the generators of a controllability matrix
(
Citations: 18
)
F Uhlig
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 85, no. 1, pp. 203209, 1987
Quality of the Solution Sets of ParameterDependent Interval Linear Systems
(
Citations: 8
)
E. Popova
Journal:
Zammzeitschrift Fur Angewandte Mathematik Und Mechanik
, vol. 82, no. 10, pp. 723727, 2002
Visualizing parametric solution sets
(
Citations: 5
)
E. D. Popova
,
W. Krämer
Journal:
Bit Numerical Mathematics  BIT
, vol. 48, no. 1, pp. 95115, 2008
Standardized notation in interval analysis
(
Citations: 25
)
R. Baker Kearfott
,
Mitsuhiro T. Nakao
,
Arnold Neumaier
,
Siegfried M. Rump
Journal:
Reliable Computing
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Citations
(1)
The thermoelectrically powered heater
D. J. Chou
,
C. W. Lu
Conference:
Energy Conversion Engineering Intersociety Conference  IECEC
, 1989