Question: Problem 1. Consider the following data points xi | 0 | 0.5 |1|2|3 vi 0 0.25 1 1-1 Find the following interpolating polynomials and use

Problem 1. Consider the following data points xi | 0 |

Problem 1. Consider the following data points xi | 0 | 0.5 |1|2|3 vi 0 0.25 1 1-1 Find the following interpolating polynomials and use MATLAB to graph the interpolants and the data points. a) The piecewise linear Lagrange interpolating polynomial 1() b) The piecewise quadratic Lagrange interpolating polynonial ). c) Newtons divided difference interpolation pa(a) of degree $ 4. d) The natural cubic spline s(x)

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