Clear Filters
Clear Filters

How to do a Taylor expansion with a matrix

30 views (last 30 days)
I have tried the official matlab website that describes the Taylor expansion, but it doesn't work!
G = [0,4;4,0];
T = taylor(exp(G));
error message "Function 'taylor' (input argument of type 'double') is undefined."
I would like to know the result of infinite convergence separately.
I would be glad if you could tell me!
  2 Comments
Ashutosh
Ashutosh on 26 May 2023
I am not sure I understand your query. A Taylor expansion can be constructed for a function of some variable x. What you are feeding into the Taylor function taylor(), seems to be a constant. You can't have a Taylor expansion, approximation or anything for a constant.
kuroshiba
kuroshiba on 1 Jun 2023
I see, I had mistakenly thought that Taylor expansion could be done with constants!
Thanks for your comments pointing that out!

Sign in to comment.

Accepted Answer

Torsten
Torsten on 26 May 2023
Edited: Torsten on 26 May 2023
Maybe you mean:
G = [0,4;4,0];
Gexp = expm(G)
Gexp = 2×2
27.3082 27.2899 27.2899 27.3082
or
syms t
G = [0,4;4,0]*t;
Gexp = simplify(taylor(expm(G),t,'ExpansionPoint',1))
Gexp = 
Gexp = simplify(subs(expm(G),t,1))
Gexp = 
  1 Comment
kuroshiba
kuroshiba on 1 Jun 2023
That is what I wanted to know! Thank you!
I'm sorry for the lack of words and understanding that bothered you.

Sign in to comment.

More Answers (2)

KSSV
KSSV on 26 May 2023
syms x
f = exp(x)
f = 
T = taylor(f)
T = 
In place of x substitue each value of G.

John D'Errico
John D'Errico on 26 May 2023
You cannot compute the Taylor series of a constant. You CAN compute a Taylor series, and then evaluate it at that constant value, since the truncated series is then a polynomial.
Will only a few terms from that Taylor series be close to yielding a convergent result? This is something you need to consider, and that is a big part of your homework where you have shown no effort. The eigenvalues of G will be an important factor.
G = [0,4;4,0];
eig(G)
ans = 2×1
-4 4
So, given that, will a simple Taylor series for exp(x) converge well for x==4 (or x==-4, for that matter)? How many terms would you expect that to require? Why did I compute the eigenvalues of G here? How are they pertinent?
  1 Comment
Paul
Paul on 1 Jun 2023
Isn't the Taylor series of function that's a constant just the constant?
syms f(x)
f(x) = sym(8);
taylor(f(x))
ans = 
8

Sign in to comment.

Products


Release

R2022b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!