On computing of block ILU preconditioner for block tridiagonal systems

We present the recurrence formulas for computing the approximate inverse factors of tridiagonal and pentadiagonal matrices using bordering technique. Resulting algorithms are used to approximate the inverse of pivot blocks needed for constructing block ILU preconditioners for solving the block tridiagonal linear systems, arising from discretization of partial differential equations. Resulting preconditioners are suitable for parallel implementation. Comparison with other methods are also included.