” data留学生程序 写作、 辅导Matlab课程设计程序Homework 2 All rights reserved.Problem 1Consider the polynomial interpolation for the following data pointsx 0 2 3 4y 7 11 28 63(a). Write down the linear system in matrix form for solving the coecientsai (i = 0, , n)of the polynomial pn(x).(b). Use the Lagrange interpolation process to obtain a polynomial to approximate these datapoints.Problem 2The Polynomial p(x) = x4x3 + x2x + 1 has the values shown.x -2 -1 0 1 2 3p(x) 31 5 1 1 11 61Find a polynomial q(x) that takes these values (you dont need expand it):x -2 -1 0 1 2 3q(x) 31 5 1 1 11 30(Hint: This can be done with little work. Try the Lagrange form.)Problem 3data留学生作业 写作、 辅导Matlab课程设计作业Let P3(x) be the interpolating polynomial for the data (0, 0), (0.5, y), (1, 3) and (2, 2). Find y ifthe coecientof x3 in P3(x) is 6.Matlab Problem 1Ccompute the numerical derivative of f(x) = xex on [0, 1] by using the formula below.Write a matlab code to test the convergence order numerically (Please hand in your code).Matlab Problem 2Consider the polynomial interpolation On the interval [1,1] with Two types of f(x):f1(x) = cos(x), f2(x) = 11 + x2 .Write a matlab script for computing the error of polynomial interpolations of fi(x), and fillErrn for dierent polynomial interpolations in the following table. The error of polynomialinterpolation is defined asEn = kpn(x)f(x)kwhere x is a Vector representing the uniform grid points on [1,1].Hint: Using the Element-wise division ./ and the element-wise power .^.What to hand in? Your script file to get the results1cHomework 2 All rights reserved.n f1(x) f2(x)Naive En Lagrange En Naive En Lagrange En如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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