LU Decomposition Method: Decomposing a Matrix Example: Part 1 of 2

Learn via an example how to take a square matrix [A] and decompose it into LU form.

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Education

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• LU
• decomposition
• decomposing
• to
• numerical
• methods
• numericalmethodsguy

[MrMuesli]

first step is to change row 1 with row 3 - and the solution vector is changed from (x1, x2, x3) to (x3, x2, x1) - than it's easier to calculate it - and more accurate if you do it with the computer

[numericalmethodsguy]

@MrMuesli The example is solely for explaining the algorithm. We do not change rows, as we follow the Naive Gauss Elimination Forward Elimination steps to find A=LU. If we change the rows for less round-off error, we follow the Gaussian Elimination with Partial Pivoting, and would get PA=LU, where P is called the perturbation matrix. Exchanging rows does not change the unknown vector.

[sammyjny]

When we use LU Decomposition to solve a system of equations, how do we guarantee its uniqueness? Will different LU Decompositions give different solutions to the same system of equations?

[numericalmethodsguy]

@sammyjny The system of equations will have a unique solution if the coefficient matrix is nonsingular. That has nothing to do with the uniqueness of LU Decomposition.

[esramer]

thank you from Jordan :) 

[TimpBizkit]

Ax = b we know A and b and want to find x

A = LU the L has 1s for the main diagonal

Ly = b, find y

Ux = y, find x

[sabatonchik]

39,376 students have bad teachers at their universities :)

[Ninjarni]

Thankyou, from Australia

[vitfc]

Great Class, congratulations!

[xelink]

this video was GREAT.

the 2nd half is giving me a server error... I have a quiz on this in 28.5 hours... ehh I'll learn elsewhere.