Relatório de estágio supervisionado Laboratório de Sistemas Embarcados e Computação Pervasiva (EMBEDDED).

Abstract

This report aims to describe the activities developed during the Supervised Internship period carried out at the Embedded Systems and Pervasive Computing Laboratory, which took place from July 17, 2024 to September 12, 2024, totaling a workload of 330 hours. The internship's main objective was the hardware implementation of a matrix inversion system, using fixed-point arithmetic, applied to FPGAs. Matrix inversion is widely used in linear algebra algorithms, being essential in areas such as solving linear systems, computing eigenvalues, and stability analysis. During the internship, the intern was assigned activities that involved modeling and hardware implementation, as well as the development of fixed-point multiplication, division, and square root modules, necessary for the efficient operation of the system. The main challenge of this project was the adaptation of traditional linear algebra algorithms, usually implemented in floating point, for fixed-point operations. This approach is necessary to ensure efficient use of hardware resources, reducing complexity and power consumption. Furthermore, the implementation of a state machine to control the QR decomposition and upper triangular matrix inversion steps was a key part of ensuring that the system operated correctly and in real time. The internship provided the intern with an understanding of hardware techniques applied to linear algebra problems and hands-on experience in implementing complex digital systems, allowing for significant technical development in the area of digital design.