Computational methods for inverses of tridiagonal matrices

• Grant number: 17/07767-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2017
• End date: May 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Fabio Vinicius Goes Amaral
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

In this project, we will analyses theoretical aspects and we will implement computational methods for computing inverses of tridiagonal matrices. In the first stage of this project, the study will be directed for a special type of tridiagonal matrices: Symmetric and Positive Definite (SPD). The student will investigate a matrix decomposition which can be applied for efficiently obtaining an inverse of a SPD matrix. This strategy, which is known as Conjugate Decomposition, was recently proposed in the literature, and it will be carefully analyzed in this research project. Finally, the subsequent stage will consisting the study of explicit formulas for computing the inverses of generalized tridiagonal matrices. Theoretical analyses will be supplemented with numerical solutions in order to give more knowledge for the student in the scientific computing area.