Speciální třídy P-matic v intervalovém prostředí
| Thesis title in Czech: | Speciální třídy P-matic v intervalovém prostředí |
|---|---|
| Thesis title in English: | Special classes of P-matrices in the interval setting |
| Key words: | B-matice|Doubly B-matice|B^R_π-matice|Intervalová analýza|Intervalová matice|P-matice |
| English key words: | B-matrix|Doubly B-matrix|B^R_π-matrix|Interval analysis|Interval matrix|P-matrix |
| Academic year of topic announcement: | 2020/2021 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Applied Mathematics (32-KAM) |
| Supervisor: | prof. Mgr. Milan Hladík, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 27.10.2020 |
| Date of assignment: | 27.10.2020 |
| Confirmed by Study dept. on: | 09.06.2021 |
| Date and time of defence: | 02.07.2021 09:00 |
| Date of electronic submission: | 18.05.2021 |
| Date of submission of printed version: | 27.05.2021 |
| Date of proceeded defence: | 02.07.2021 |
| Opponents: | Mgr. Peter Zeman |
| Guidelines |
| - prozkoumat speciální třídy P-matic
- adaptovat jejich charakterizace na případ intervalové matice - vyšetřit jejich vlastnosti |
| References |
| [1] Milan Hladík. On relation between P-matrices and regularity of interval matrices. In N. Bebiano, editor, Applied and Computational Matrix Analysis, Springer Proceedings in Mathematics & Statistics, pp. 27-35, 2017.
[2] Milan Hladík. An overview of polynomially computable characteristics of special interval matrices. In O. Kosheleva et al., editor, Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications, pp. 295-310, Springer, 2020. [3] J.M. Pena. A class of P-matrices with applications to the localization of the eigenvalues of a real matrix. SIAM J. Matrix Anal. Appl., 22(4):1027-1037, 2001 [4] Michael J. Tsatsomeros. Generating and detecting matrices with positive principal minors, in L. Li, ed., Focus on Computational Neurobiology, Nova Science Publishers, pp. 115-132, 2004 |
| Preliminary scope of work |
| P-matice jsou důležité matice s mnoha pěknými vlastnostmi, mj. zaručují, že úloha lineární komplementarity má jednoznačné řešení. Rozpoznávání, zda je daná matice P-maticí, je však NP-těžké. Proto byly navrženy různé speciální třídy P-matic, které jsou snadněji ověřitelné. Cílem práce je prozkoumat tyto speciální třídy pro případ intervalové matice, adaptovat podmínky na rozpoznávání jednotlivých typů matic a vyšetřit jejich vlastnosti. Není potřeba se zabývat H-maticemi a positivně definitními maticemi, protože ty jsou studovány podrobně. |
| Preliminary scope of work in English |
| P-matrices are important matrices with many nice properties, e.g. they ensure that the linear complementarity problem has a unique solution. Recognition, whether a given matrix belongs to the class of P-matrices, is however NP-hard. Therefore various special classes have been proposed, which are more easily verifiable. The objective of this thesis is to inspect some of these special classes in the interval setting, to adapt the conditions of recognition of the individual types of matrices and to examine their properties. |