code to implement continuous least square

Question

sam2021 2020-2-28

0
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https://ww2.mathworks.cn/matlabcentral/answers/508145-code-to-implement-continuous-least-square

回答： Dinesh Yadav 2020-3-2

Write Matlab code to implement the continuous least squares method of finding the best-fit polynomial of degree n for a given function f on the interval [a, b]. Again, you may not use the Matlab command polyfit or anything similar. Populate a matrix and vector and solve the resulting matrix-vector equation. Once you have solved the matrix-vector equation, you may then use the polyval function. The inputs should be contained in a Matlab function file called clsin.m, which should contain, for example,

function [n f a b] = clsin()

syms x;

n = 5;

f = sqrt(x);

a = 0;

b = 1;

end

In this example, we are trying to fit a polynomial of degree 5 to the function f(x) = √x on the interval [0,1]. Your output should be a picture, showing both the original function f and its least squares polynomial approximation, both only on the interval [a, b]. The Matlab command fplot (in the symbolic toolbox) may prove to be handy.

I am really struggling with this problem. We cannot use polyfit or anything similar. Any help on this problem would be appreciated.