#lu factorization

Illustrating the LU algorithm with pivots by example

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Two previous examples of LU factorizations were given. I found one more to be the key to understanding how to implement this as a matlab algorithm, required for our problem set.

A matrix that contains both pivots and elementary matrix operations is

\begin{equation}\label{eqn:luAlgorithm:20} M= \begin{bmatrix} 0 & 0 & 2 & 1 \\ & 0…

Numerical LU example where pivoting is required

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I’m having trouble understanding how to apply the LU procedure where pivoting is required. Proceeding with such a factorization, doesn’t produce an LU factorization that is the product of a lower triangular matrix and an upper triangular matrix. What we get instead is what looks like a permutation of a lower triangular matrix…

Numeric LU factorization example

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To get a better feel for LU factorization before attempting a numeric implementation, let’s look at a numeric example in detail. This will strip some of the abstraction away.

Let’s compute the LU factorization for

\begin{equation}\label{eqn:luExample:20} M = \begin{bmatrix} 5 & 1 & 1 \\ 2 & 3 & 4 \\ 3 & 1 & 2 \\ \end{bmatrix}. \e…