MATLAB Function Reference Volume 1: A - E - Bad Request

cholinc
Examples Example 1.
2-250
gets rid of the symptoms of the problem, but it does not solve it. The
preconditioner may not be singular, but it probably is not useful, and a warning
message is printed.
The Cholesky-Infinity factorization is meant to be used within interior-point
methods. Otherwise, its use is not recommended.
Start with a symmetric positive definite matrix, S.
S = delsq(numgrid('C',15));
S is the two-dimensional, five-point discrete negative Lapacian on the grid
generated by numgrid('C',15).
Compute the Cholesky factorization and the incomplete Cholesky factorization
of level 0 to compare the fill-in. Make S singular by zeroing out a diagonal entry
and compute the (partial) incomplete Cholesky factorization of level 0.
C = chol(S);
R0 = cholinc(S,'0');
S2 = S; S2(101,101) = 0;
[R,p] = cholinc(S2,'0');
Fill-in occurs within the bands of S in the complete Cholesky factor, but none
in the incomplete Cholesky factor. The incomplete factorization of the singular
S2 stopped at row p = 101 resulting in a 100-by-139 partial factor.
D1 = (R0'*R0).*spones(S)-S;
D2 = (R'*R).*spones(S2)-S2;
D1 has elements of the order of eps, showing that R0'*R0 agrees with S over its
sparsity pattern. D2 has elements of the order of eps over its first 100 rows and
first 100 columns, D2(1:100,:) and D2(:,1:100).