Figure Properties - SERC

thresh is the pivot threshold between 0 (forces diagonal pivoting) and 1, the
default, which always chooses the maximum magnitude entry in the column to
be the pivot. thresh is desribed in greater detail in lu.
luinc(X,options) is the same as luinc(X,droptol) if options has droptol as
its only field.
[L,U] = luinc(X,options) returns a permutation of a unit lower triangular
matrix in L and an upper trianglar matrix in U. The product L*U is an
approximation to X. luinc(X,options) returns the strict lower triangular part
of the factor and the upper triangular factor embedded within the same matrix.
The permutation information is lost.
[L,U] = luinc(X,options) is the same as luinc(X,droptol) if options has
droptol as its only field.
[L,U,P] = luinc(X,options) returns a unit lower triangular matrix in L, an
upper triangular matrix in U, and a permutation matrix in P. The nonzero
entries of U satisfy
abs(U(i,j)) >= droptol*norm((X:,j)),
with the possible exception of the diagonal entries which were retained despite
not satisfying the criterion. The entries of L were tested against the local drop
tolerance before being scaled by the pivot, so for nonzeros in L
abs(L(i,j)) >= droptol*norm(X(:,j))/U(j,j).
The product L*U is an approximation to the permuted P*X.
[L,U,P] = luinc(X,options) is the same as [L,U,P] = luinc(X,droptol) if
options has droptol as its only field.
Remarks These incomplete factorizations may be useful as preconditioners for solving
large sparse systems of linear equations. The lower triangular factors all have
1s along the main diagonal but a single 0 on the diagonal of the upper
triangular factor makes it singular. The incomplete factorization with a drop
tolerance prints a warning message if the upper triangular factor has zeros on
the diagonal. Similarly, using the udiag option to replace a zero diagonal only
gets rid of the symptoms of the problem but does not solve it. The
preconditioner may not be singular, but it probably is not useful and a warning
message is printed.
luinc
2-1395