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Rank one interval enclosure of the parametric united solution set

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Abstract

Consider linear algebraic systems \(A(p)x=b(p)\), where the matrix and the right-hand side vector depend linearly on a number of parameters \(p=(p_1,\ldots , p_K)^{\top }\) that vary within given intervals. For each interval parameter, the structure of the dependencies can be presented by a finite sum of rank one matrices. This representation implies new more general and powerful sufficient conditions for regularity of a parametric interval matrix and a flexible general methodology for solving parametric interval linear systems with an expanded scope of applicability.

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Notes

  1. The abbreviation “parametric interval linear system” is used in this and other articles as a synonym of the abbreviation “interval parametric linear system” used, e.g., in [4, 5], although the second one might be more appropriate.

  2. An exception is the method based on the methodology presented in [17].

  3. Overestimation is defined at the end of Example 4.1.

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Acknowledgements

This work is partly supported by the Grant BG05M2P001-1.001-0003 of the Bulgarian Ministry of Science and Education.

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  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Block 8, 1113, Sofia, Bulgaria

    Evgenija D. Popova

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  1. Evgenija D. Popova
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Correspondence to Evgenija D. Popova.

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Communicated by Lars Eldén.

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Popova, E.D. Rank one interval enclosure of the parametric united solution set. Bit Numer Math 59, 503–521 (2019). https://doi.org/10.1007/s10543-018-0739-4

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