Interpolación | 16/35 | UPV

Title: Interpolation Automatic description: In this video, the expert explains the concept of interpolation, a method used in mathematics to approximate functions based on known data sets. She exemplifies its usefulness in situations such as the analysis of experimental measurements or the approximate solution of differential equations. Interpolation involves finding a simple function that passes through a given set of points. When a value is found within the range of these points, it is called interpolation, while when it is found outside the range, it is called extrapolation. Polynomial interpolation is introduced as a technique for constructing a polynomial that matches data at specific points. This polynomial, of degree less than or equal to the number of points minus one, is determined by solving a linear system whose solution is unique if the points are distinct, thanks to the Vandermonde determinant. In addition, the expert presents Lagrange polynomials, another way of expressing the interpolating polynomial useful in differentiation and numerical integration. These are calculated using a product involving the given points and allow the value of the function to be obtained at any point within the analyzed interval. The video conference includes graphical examples of how this process would be performed, including calculating the temperature at a given time with hourly data, and demonstrates that the Lagrange polynomial is a valid interpolant for all data points. Author: Rosello Ferragud Maria Dolores Course: This video is video 16/35 of the MOOC course Numerical Methods for Mathematics with Octave.    • MOOC Introducción a la solución numérica d...   Sign up at: https://upvx.es/courses/course-v1:edx... Polytechnic University of Valencia (UPV): https://www.upv.es More videos at:    / valenciaupv   Access our MOOCs: https://upvx.es #interpolation #interpolatingpolynomial