Combine upper, lower, and diagonal matrix?

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SUMMARY

The discussion focuses on solving a matrix that combines diagonal, upper, and lower triangular components using MATLAB. The provided example illustrates a 4x4 matrix with specific values, questioning whether it is feasible to solve the upper and lower triangles separately before combining results. Additionally, participants seek clarification on the term "solve" in the context of matrix operations, indicating a need for a deeper understanding of matrix decomposition and solution methods.

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  • Knowledge of triangular matrices (upper and lower)
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sarahfh
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If you have a matrix that is a combination of a diagonal, upper, and lower matrix - what is the best way to solve it? (I use MATLAB for matrix work)

Example:
5 1 0 0 x1 1
-1 5 1 0 x2 2
0 -1 5 1 x3 3
0 0 -1 5 x4 4

Is it possible to solve the upper triangle and lower triangle and then combine them?
Would it be possible to solve it quicker if the all three diagonals were the same (as above)?
 
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I can't understand the example you have written. What does an "x" denote?

What do you mean by "solve" a matrix? Please clarify your example and I think someone will be able to help you.
 

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