The paper concerns preconditioning by incomplete block factorization of the type \(PD^{-1}P^ T\) where \(D\) is a block diagonal and \(P\) is a twisted block triangular matrix. More precisely, \(P\) has nonzero blocks only in the diagonal positions and the positions \((i,i-1)\) for \(i\leq k\) and \((i,i+1)\) for \(k\leq i\), where \(k\) is a parameter.
For this type of incomplete factorization, results concerning stability of factorization, error due to incomplete factorization and spectral characterization of the preconditioning effect are presented and the new type of factorization is compared with the standard incomplete block \(LD^{-1}L^ T\) factorization.
The main reason for introducing this new type of incomplete factorization is the possibility of parallel processing. For a two processor parallel computer the speed up of about 2 is reached in the presented numerical experiments.