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Math 105LA Computer Assignment 5

Due Fri 11/5

Implement the LU factorization algorithm. Algorithm for LU factorization:

INPUT : Matrix Dimension n, the matrix A and method choice Doolittle or Crout.

OUTPUT : L and U, or the failure message

Step 1: Select l11 and u11 satisfying l11u11 = a11 based on the choice If l11u11 = 0, then output (’factorization impossible’); STOP

Step 2: For j = 2 : n, set

u1j = a1j/l11, lj1 = aj1/u11

Step 3: For i = 2 : n − 1, do Steps 4 and 5

Step 4: Select lii and uii satisfying liiuii = aii − ∑i−1

k=1 likuki based on the choice

If liiuii = 0, then output (’factorization impossible’); STOP

Step 5: For j = i + 1 : n, set

uij =

[ aij −

i−1∑ k=1

likukj

] /lii, lji =

[ aji −

i−1∑ k=1

ljkuki

] /uii

Step 6: Select lnn and unn satisfying lnnunn = ann − ∑n−1

k=1 lnkukn based on the choice

Step 7: Output L and U; STOP

1

Use the algorithm with both methods to factorize

A =

 

1 1 0 3 2 1 −1 1 3 −1 −1 2 −1 2 3 −1

  . (1)

2

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