Hourglass Matrix: Its Quadrant Interlocking Factorization Using Modified Cramer’s Rule And Its Mixed Graph
| dc.contributor.author | Babarinsa, Olayiwola Isaac | |
| dc.date.accessioned | 2020-06-29T06:15:19Z | |
| dc.date.available | 2020-06-29T06:15:19Z | |
| dc.date.issued | 2019-06 | |
| dc.description.abstract | Hourglass matrix has been synonymously referring to 𝑍-matrix for decades without properly considering the components of their entries. In this research, it is established that hourglass matrix is, in fact, a subset of 𝑍-matrix. An hourglass matrix is obtained by carrying out row interchange at every stage of the Quadrant Interlocking Factorization (𝑄𝐼𝐹), when necessary, to ensure the computed entries of the matrix are restricted to be nonzero. In general, any 2×2 linear systems in 𝑄𝐼𝐹 algorithm is solved using Cramer's rule. Cramer's rule is used to ensure that the 𝑄𝐼𝐹 does not breakdown at every stage of the factorization process. Though Cramer's rule allows complete substitution of column vector to the coefficient matrix, the modified Cramer's rule derived in this thesis considered the column vector together with the coefficient matrix for solving simple linear systems. The proposed methods are efficient for 2×2 linear system and are shown to be equivalent to classical Cramer's rule, but differ in their relative residual measurement. The presented results show that there is no tangible difference in performance time between the Cramer's rule and its modifications in the 𝑄𝐼𝐹 of dense nonsingular square matrices. Furthermore, the Frobenius norm of the modified methods in the factorization are shown to be better than Cramer's rule, irrespective of the version of MATLAB used. Besides, the potential applications of hourglass matrix and its QIF in Markov chains and in lattice-based cryptography over 𝑍-matrix and its WZ factorization are highlighted. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/9764 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | Hourglass Matrix | en_US |
| dc.subject | Quadrant Interlocking | en_US |
| dc.title | Hourglass Matrix: Its Quadrant Interlocking Factorization Using Modified Cramer’s Rule And Its Mixed Graph | en_US |
| dc.type | Thesis | en_US |
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