Solving a matrix equation?

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Matt
Matt 2015-3-20
回答： Karthikeyan S 2022-4-20
I'm trying to solve the following matrix equation using MATLAB:
AU + UB = C
A, B, and C are known matrices and I want to solve for the matrix U. A and B are square, symmetric, and tridiagonal. Does anyone have advice on how to use MATLAB to efficiently solve this system? Thank you for any help in advance!

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采纳的回答

Torsten
Torsten 2015-3-20
Look at 5.1.10 under
http://www.math.uwaterloo.ca/~hwolkowi//matrixcookbook.pdf
for a solution.
Enter
help kron
to get information on how to form the Kronecker tensor product in MATLAB.
Best wishes
Torsten.
  1 个评论
Matt
Matt 2015-3-20
Thank you for your answer! While your solution works, I discovered that MATLAB has a straightforward command for solving this system - see my answer if interested.

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更多回答（3 个）

Matt
Matt 2015-3-20
For anyone who may stumble upon this in the future, turns out my system is the Sylvester equation. Its solution has been implemented in MATLAB starting in version 2014a:
http://www.mathworks.com/help/matlab/ref/sylvester.html
Pramod Palayangoda
Pramod Palayangoda 2021-1-23
1. Consider the following system of equations.
2𝒙𝟏 + 𝟓𝒙𝟐 + 𝟓𝒙𝟑 = 𝟓
4𝒙𝟏 − 𝒙𝟐 + 𝟐𝒙𝟑 = −𝟔
−𝟐𝒙𝟏 + 𝟑𝒙𝟐 − 𝒙𝟑 = 𝟏𝟏
i) Form a matrix for the coefficients of the above system and name it as A.
ii) Find the determinant of A.
iii) Find the inverse of A.
iv) Form a matrix for the right hand values and name it as B
v) Solve the above system.
Karthikeyan S
Karthikeyan S 2022-4-20
2𝒙𝟏 + 𝟓𝒙𝟐 + 𝟓𝒙𝟑 = 𝟓

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