Theoretical and computational studies of the least square method and its variations

• Grant number: 21/04506-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2021
• End date: June 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Daniel Henrique Serezane Pereira
• 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 investigate the least squares method for approximating discrete data. Initially, classic Linear Algebra topics will be analyzed, such as orthogonalization, matrix decompositions, eigenvalues and eigenvectors, etc. After this stage, the student will implement the most known techniques for computationally solving the least squares methods for data approximation. Lastly, special attention will be given to the method's applications and variations involving artificial intelligence.