Use MATLAB to calculate the Taylor series expansion coefficients of polynomials

matlab calculates the coefficients of the Taylor series expansion of polynomials

clear;clc;

syms x a;

m=5；%Change it yourself

y=(11/6-3*x 3/2*x^2-1/3*x^3)^a

f=taylor(y,m 1,x);

w=sym(zeros(m 1,1));

w(1)=subs(f,x,0);

f=f-w(1);

for n=m:-1:2

w(n 1)=subs(f-subs(f,x^n,0),x^n,1);

f=f-w(n 1)*x^n;

end

w(2)=subs(f,x,1)

Note that because the matlab array subscript starts from 1, here w(1) is a constant term and w(2) is a linear term, so By analogy,

y=w(1) w(2)*x w(3)*x^2 .... w(m 1)*x^m

How to solve the problem of undetermined coefficients in matlab

【1】Transform the function

>>f=sym('2*x^3 3*x^2 21*x 4-(3*a*x^3 b*x^2 c*x d)=0')

f =

2*x^3 3*x^2 21*x 4-(3*a*x^3 b*x^2 c*x d)=0

【2】Use collect to merge similar items

>>ff=collect(f):

(2-3*a)*x^3 (3-b)*x^2 (21-c)*x 4-d = 0

[3] Use maple to extract polynomial coefficients. If there are many, you can use loop statements.

>>c3=maple('coeff',ff,x,3)

c3 =2-3*a

>>c1=maple('coeff',ff,x,1)

c1 =21-c

>>c2=maple('coeff',ff,x,2)

c2 =3-b

>>c0=maple('coeff',ff,x,0)

c0 =4-d

Replenish:

This time it turned out like this, the program worked, but I’m not very satisfied. How about we sort it out together?

syms a b c d x

%【1】Transform the function

f=sym('2*x^3 3*x^2 21*x 4-(3*a*x^3 b*x^2 c*x d)')

N=3;

for i=0:N

temp=maple('coeff',f,x,N-i);

cp(1,i 1)={temp};

end

celldisp(cp);

Additional addition: This time it is finally solved, but it looks very stupid and not very ideal. I just make do with it. Of course, I believe it can be modified to be beautiful.

syms a b c d x

f=sym('2*x^3 3*x^2 21*x 4-(3*a*x^3 b*x^2 c*x d)')

N=3;

for i=0:N

temp=maple('coeff',f,x,N-i);

temp1(i 1)=temp;

end

cp=temp1

a=solve(cp(1)), b=solve(cp(2)), c=solve(cp(3)), d=solve(cp(4))

operation result:

a =2/3

b =3

c =21

d =4

The functional formula M file for the value of polynomial Px anxn an1xn1 a1x a0 is used

First of all, the polynomial is dynamic, so this must be an input term of matlab;

Secondly, the Matlab expression of polynomials must be clear. It is to extract the coefficients of the polynomials after lowering the power to represent the polynomial. The -n degree polynomial of the polynomial is represented by an n 1-dimensional vector; for example, the polynomial 3*x^2 5 in matlab Expressed as [3 0 5];

Finally, you need to understand the matlab method of polynomial function value, which is the command polyval.

Based on the above, the M file is as follows:

function val = fpolyval(p,x)

% Function fpolyval Function: Function value val of polynomial p at x.

% The input item p is the coefficient of the polynomial arranged in descending powers;

val = polyval(p,x);

For example: 3*x^2 5 value at x=1,2

>>p=[3 0 5];

>>x=[1 2];

>>val=fpolyval(p,x)

val =

8 17

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