Estudo e implementação de técnicas de interpolação polinomial

Abstract

This works presents a comprehensive study on polynomial interpolation techniques, exploring from classical methods to more advanced approaches, such as piecewise interpolation. The main objective is to provide a solid foundation for understanding and applying the discussed techniques, in order to investigate their validity and feasibility in function approximation and data set representation, analyzing their advantages, limitations, and practical applications. For this purpose, methods such as Lagrange interpolation, Newton’s form and natural splines were explored, with computational implementation in MATLAB/Octave. The detailed analysis of polynomial interpolation techniques revealed their importance both theoretically and practically. Additionally, oscillatory phenomena that affect the fitting of a function were identified, and a solution was presented to minimize this problem. Finally, a practical example is addressed that reinforces the applicability of the theory studied throughout the work.