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Previous: Block factorization methods
Up: Incomplete Factorization Preconditioners
Previous Page: Blocking over systems of partial differential
equations
Next Page: Polynomial preconditioners
Saad [180] proposes to construct an incomplete LQ factorization
of a general sparse matrix. The idea is to orthogonalize the rows
of the matrix by a Gram-Schmidt process (note that in sparse matrices,
most rows are typically orthogonal already, so that standard Gram-Schmidt
may be not so bad as in general). Saad suggest dropping strategies for
the fill-in produced in the orthogonalization process. It turns out that
the resulting incomplete L factor can be viewed as the incomplete Choleski
factor of the matrix . Experiments show that using
in a CG
process for the normal equations:
is effective for
some relevant problems.