MATLAB Mathematics - SERC - Index of

6 Sparse Matrices
The following MATLAB functions implement the approximate minimum
degree algorithm:
• symamd — Use with symmetric matrices
• colamd — Use with nonsymmetric matrices and symmetric matrices of the
form A*A' or A'*A.
See “Reordering and Factorization” on page 6-31 for an example using symamd.
You can change various parameters associated with details of the algorithms
using the spparms function.
For details on the algorithms used by colamd and symamd, see [5]. The
approximate degree the algorithms use is based on [1].
Factorization
This section discusses four important factorization techniques for sparse
matrices:
• LU, or triangular, factorization
• Cholesky factorization
• QR, or orthogonal, factorization
• Incomplete factorizations
LU Factorization
If S is a sparse matrix, the following command returns three sparse matrices L,
U, and P such that P*S = L*U.
[L,U,P] = lu(S)
lu obtains the factors by Gaussian elimination with partial pivoting. The
permutation matrix P has only n nonzero elements. As with dense matrices, the
statement [L,U] = lu(S) returns a permuted unit lower triangular matrix and
an upper triangular matrix whose product is S. By itself, lu(S) returns L and
U in a single matrix without the pivot information.
The three-output syntax
[L,U,P] = lu(S)
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