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Decomposition of a matrix into a product of matrices with special properties. Common matrix factorizations include LU, QR, SVD, and Cholesky.
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Existence of incomplete cholesky factorization
I would suggest you the reading of Wang's thesis on the subject.
http://repository.tamu.edu/bitstream/handle/1969.1/ETD-TAMU-3135/WANG-DISSERTATION.pdf?sequence=1
Using local element stiffness matric …