Banca de DEFESA: IRIA CALINE SARAIVA COSME

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : IRIA CALINE SARAIVA COSME
DATA : 04/05/2018
HORA: 14:30
LOCAL: PoP-RN
TÍTULO:

Recursive inversion of block matrices with limited memory usage

PALAVRAS-CHAVES:

Block matrices. Low memory usage. Schur Complement. Large matrices inversion.

PÁGINAS: 100
GRANDE ÁREA: Engenharias
ÁREA: Engenharia Elétrica
RESUMO:

The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider exchanging less memory usage for more processing time in order to enable the computation of the inverse which otherwise would be prohibitive.

Therefore this work introduces a novel algorithm to compute the inverse of block partitioned matrices with a reduced memory footprint. The algorithm works recursively to invert one block of a k×k block matrix M, with Mk×k , based on the successive splitting of M. This algorithm, called BRI (Block Recursive Inverse), computes one block of the inverse at a time to limit memory usage during the entire processing.
Considering that the low memory consumption, provided by the BRI, is counterbalanced by longer processing time, this work also discusses a parallel implementation in OpenMP of the algorithm to reduce the execution time and to extend its applicability. Besides, an improvement in the sequential algorithm is analyzed.
As a practical application, the proposed algorithm was applied in the cross-validation process for Least Squares Support Vector Machines (LS-SVM), introduced by An et al. (2007). This computational procedure uses the inverse matrix calculation to find the expected labels of the test samples in the cross-validation.
Experimental results with BRI show that, despite increasing computational complexity, matrices that otherwise would exceed the memory-usage limit can be inverted using this technique.

MEMBROS DA BANCA:
Interno - 347628 - ADRIAO DUARTE DORIA NETO
Externo à Instituição - AURÉLIO RIBEIRO LEITE DE OLIVEIRA - UNICAMP
Interno - 1746084 - DANIEL ALOISE
Externo à Instituição - FRANCISCO CHAGAS DE LIMA JUNIOR - UERN
Interno - 1153006 - LUIZ AFFONSO HENDERSON GUEDES DE OLIVEIRA
Presidente - 1673543 - SAMUEL XAVIER DE SOUZA