data留学生代做、代写Matlab设计、Matlab编程语言调试

日期：2020-09-13 09:34

Homework 2 All rights reserved.

Problem 1

Consider the polynomial interpolation for the following data points

x 0 2 3 4

y 7 11 28 63

(a). Write down the linear system in matrix form for solving the coecients

ai (i = 0, ··· , n)

of the polynomial pn(x).

(b). Use the Lagrange interpolation process to obtain a polynomial to approximate these data

points.

Problem 2

The polynomial p(x) = x4

x3 + x2

x + 1 has the values shown.

x -2 -1 0 1 2 3

p(x) 31 5 1 1 11 61

Find a polynomial q(x) that takes these values (you don’t need expand it):

x -2 -1 0 1 2 3

q(x) 31 5 1 1 11 30

(Hint: This can be done with little work. Try the Lagrange form.)

Problem 3

Let P3(x) be the interpolating polynomial for the data (0, 0), (0.5, y), (1, 3) and (2, 2). Find y if

the coecient

of x3 in P3(x) is 6.

Matlab Problem 1

Ccompute 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 2

Consider the polynomial interpolation on the interval [1,

1] with two types of f(x):

f1(x) = cos(x), f2(x) = 1

1 + x2 .

Write a matlab script for computing the error of polynomial interpolations of fi(x), and fill

Errn for di↵erent polynomial interpolations in the following table. The error of polynomial

interpolation is defined as

En = kpn(x)

f(x)k

where 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 results

1

c

Homework 2 All rights reserved.

n f1(x) f2(x)

Naive En Lagrange En Naive En Lagrange En