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We represent the solution as a family of subsets, each defined by a matrix that is obtained from the given matrices by using a matrix sparsification technique. The technique exploits sparsified matrices to derive a series of new inequalities, which admit a direct solution in the form of matrices that generate their solutions. We describe a
backtracking procedure that reduces the brute-force search of sparsified matrices by skipping those, which cannot provide solutions, and thus offers an economical way to obtain all subsets in the family. The columns in the generating matrices for subsets are combined together to form a matrix, which is further reduced to have only columns that constitute a minimal generating system of the solution. We use the reduced matrix to represent a complete exact solution of the two-sided inequality under consideration in a compact vector form.
We illustrate the results with numerical examples. Extension of the approach to solve two-sided equations is also discussed.
|State||Published - 2019|
|Event||International Conference on Matrix Analysis and its Applications - Liblice, Czech Republic|
Duration: 8 Sep 2019 → 13 Sep 2019
Conference number: 8
|Conference||International Conference on Matrix Analysis and its Applications|
|Abbreviated title||MAT TRIAD 2019|
|Period||8/09/19 → 13/09/19|
Scopus subject areas
- Algebra and Number Theory
- tropical semifield
- linear inequality
- matrix sparsification
- complete solution
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Николай Кимович Кривулин (Participant)8 Sep 2019 → 13 Sep 2019
Activity: Attendance types › Participating in a conference, workshop, ...
Николай Кимович Кривулин (Speaker)9 Sep 2019
Activity: Talk types › Oral presentation