Python coding.

Theory We consider a method for interpolating a sequence of points. In other words we want to find a polynomial function P' of lowest possible degree such that P(xi)-i where r and yi are given points often they are called data measurements (xi,yi). According to theory if N+1 points are given, there is a unique polynomial of degree N which passes through these N +1 points. How to find the interpolation polynomial? Let P(x) be an N degree polynomial which interpolates the N 1 points (xi,yi In other words P( for Our task is to find the values of the coefficients c for this polyno- mial. To compute these coefficients we create the following equation system The above equation system can be written in matrix form as yi N N-1 2 ??? UN We define the matrix V, the coefficient vector c and the right-hand side y Eventually we will solve the above matrix system for the coefficients c. Task 4 Given a vector r of length N +1, write a Python function that constructs the matrix where the , are the components of the vector x (numbered from zero) Recall the function column stack can help you to stack vectors horizontally Theory We consider a method for interpolating a sequence of points. In other words we want to find a polynomial function P' of lowest possible degree such that P(xi)-i where r and yi are given points often they are called data measurements (xi,yi). According to theory if N+1 points are given, there is a unique polynomial of degree N which passes through these N +1 points. How to find the interpolation polynomial? Let P(x) be an N degree polynomial which interpolates the N 1 points (xi,yi In other words P( for Our task is to find the values of the coefficients c for this polyno- mial. To compute these coefficients we create the following equation system The above equation system can be written in matrix form as yi N N-1 2 ??? UN We define the matrix V, the coefficient vector c and the right-hand side y Eventually we will solve the above matrix system for the coefficients c. Task 4 Given a vector r of length N +1, write a Python function that constructs the matrix where the , are the components of the vector x (numbered from zero) Recall the function column stack can help you to stack vectors horizontally