MATLAB Mathematics - SERC - Index of

Sparse Matrix Operations
Cuthill-McKee ordering is concentrated within the band, but it is almost as
extensive as the first two orderings. For the approximate minimum degree
ordering, the relatively large blocks of zeros are preserved during the
elimination and the amount of fill-in is significantly less than that generated
by the other orderings. The spy plots below reflect the characteristics of each
reordering.
0
Original
0
Reverse Cuthill−McKee
0
Minimum Degree
10
10
10
20
20
20
30
30
30
40
40
40
50
50
50
60
0 10 20 30 40 50 60
nz = 1022
60
0 10 20 30 40 50 60
nz = 968
60
0 10 20 30 40 50 60
nz = 636
Cholesky Factorization
If S is a symmetric (or Hermitian), positive definite, sparse matrix, the
statement below returns a sparse, upper triangular matrix R so that R'*R = S.
R = chol(S)
chol does not automatically pivot for sparsity, but you can compute
approximate minimum degree and profile limiting permutations for use with
chol(S(p,p)).
Since the Cholesky algorithm does not use pivoting for sparsity and does not
require pivoting for numerical stability, chol does a quick calculation of the
amount of memory required and allocates all the memory at the start of the
factorization. You can use symbfact, which uses the same algorithm as chol,
to calculate how much memory is allocated.
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