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Generalized solution sets of the interval generalized Sylvester matrix equation \(\sum_{i=1}^p\mathbf A_iX_i+\sum_{j=1}^qY_j\mathbf B_j=\mathbf C\) and some approaches for inner and outer estimations. (English) Zbl 1368.15012

Summary: In this work, we extend the concept of generalized solution sets that is introduced for the first time by S. P. Shary [Reliab. Comput. 2, No. 1, 3–33 (1996; Zbl 0853.65048); ibid. 5, No. 3, 323–335 (1999; Zbl 0947.65033)], to the interval generalized Sylvester matrix equation \(\sum_{i=1}^p\mathbf A_iX_i+\sum_{j=1}^qY_j\mathbf B_j=\mathbf C\). Then AE-solution sets for this equation will be characterized and we develop some approaches (called algebraic approaches) in which the inner and outer estimation problems for some special cases of AE-solution sets reduce to problems of computing algebraic solutions of some auxiliary interval equations. Also we present a numerical technique that is an extension of the well-known interval Gauss-Seidel method for outer estimation of the solution set.

MSC:

15A24 Matrix equations and identities
65F30 Other matrix algorithms (MSC2010)
65G40 General methods in interval analysis

Software:

INTLAB
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