## schur_luinc

LU incemental.

LU incemental.

[a, aa, LT, UT, PT] = schur_luinc(a, b, L, U, P, A12, A21, A22, varargin)

Performs an incremental-type LU factorization on an augmented matrix [A11 A12; A21 A22], where PA = LU, A11 mxm, A12 mxn, A21 nxm and A22 nxn. To factorize A11 do [L, U, P] = lu(A11). The factorization of A22 is done without considering the elements of A12 for pivoting. Nevertheless, A12 is updated according to the factorization on A11.

a = previous solution of the problem. b = rhs of the system. L = lower triangular factor from LU factorization of A11. U = upper triangular factor from LU factorization of A11. P = permutation matrix from LU factorization of A11. A12 = right-upper block for augmented matrix. A21 = left-lower block for augmented matrix. A22 = right-lower block for augmented matrix.

precond = use precond or not ('no', 'ilu', 'diag'). for 'ndiad' define: 'numbd' (number of diagonals); for 'ilu' define: 'milu', 'typeilu', 'droptol', 'thresh' and 'udiag'.

a = next solution of the augmented problem. aa = coefficients of the error estimative. LT = augmented matrix lower triangular factor. UT = augmented matrix upper triangular factor. PT = augmented matrix permutation matrix.

schur_luinc2, schur_nflu and schur_iter.