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Evolution of Interval Eigenvalue Problems and its Applications to the Uncertain Dynamic Problems
Abstract In this article, we accumulate theories and computing procedures to find eigenvalue bounds for interval matrices. Also, we have pointed out the computational complexity and applications of interval eigenvalue problems. Computing exact eigenvalue for the general interval matrices is an NP-hard problem. Various eigenvalue bounds for symmetric, non-symmetric, and complex interval matrices are included here. The article attempts to present some of the important methods proposed by various authors in one place, analyze them, and then final observations are made. In this respect, each of the methods has been addressed by taking simple example problems of interval matrices so that readers may understand the philosophy of those methods. Further, the increase of tightness of the solutions is also discussed. The interlinks of their development and gaps among them are highlighted.
Evolution of Interval Eigenvalue Problems and its Applications to the Uncertain Dynamic Problems
Abstract In this article, we accumulate theories and computing procedures to find eigenvalue bounds for interval matrices. Also, we have pointed out the computational complexity and applications of interval eigenvalue problems. Computing exact eigenvalue for the general interval matrices is an NP-hard problem. Various eigenvalue bounds for symmetric, non-symmetric, and complex interval matrices are included here. The article attempts to present some of the important methods proposed by various authors in one place, analyze them, and then final observations are made. In this respect, each of the methods has been addressed by taking simple example problems of interval matrices so that readers may understand the philosophy of those methods. Further, the increase of tightness of the solutions is also discussed. The interlinks of their development and gaps among them are highlighted.
Evolution of Interval Eigenvalue Problems and its Applications to the Uncertain Dynamic Problems
Maiti, Suman (author) / Chakraverty, Snehashish (author)
2022
Article (Journal)
Electronic Resource
English
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