MATH 372 -- Numerical Linear Algebra
LU factorization in MATLAB

Reading the following commands:

format long

A = [ 2.222 16.710 9.612; -1.5611 5.1792 -1.6855; 3.3330 15920 10.333]

[L,U,P] = lu(A)

P'*L*U

AS = sparse(A);

[L,U,P] = lu(AS,0);  <- LU factorization with pivot "threshold"
                        threshold = 0 <=> no pivoting
                        threshold = 1 <=> full column pivoting (default)

full(L)
full(U)
full(P)

MATLAB output:

A =

   1.0e+04 *

   0.00022220000000   0.00167100000000   0.00096120000000
  -0.00015611000000   0.00051792000000  -0.00016855000000
   0.00033330000000   1.59200000000000   0.00103330000000


L =

   1.00000000000000                  0                  0
   0.66666666666667   1.00000000000000                  0
  -0.46837683768377  -0.70416190339177   1.00000000000000


U =

   1.0e+04 *

   0.00033330000000   1.59200000000000   0.00103330000000
                  0  -1.05966233333333   0.00027233333333
                  0                  0   0.00050719054474


P =

     0     0     1
     1     0     0
     0     1     0


ans =

   1.0e+04 *

   0.00022220000000   0.00167100000000   0.00096120000000
  -0.00015611000000   0.00051792000000  -0.00016855000000
   0.00033330000000   1.59200000000000   0.00103330000000


ans =

   1.0e+02 *

   0.01000000000000                  0                  0
  -0.00702565256526   0.01000000000000                  0
   0.01500000000000   9.39468853029457   0.01000000000000


ans =

   1.0e+03 *

   0.00222200000000   0.01671000000000   0.00961200000000
                  0   0.01691906543654   0.00506755724572
                  0                  0  -4.76489719330198


ans =

     1     0     0
     0     1     0
     0     0     1

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