Factored sparse approximate inverse of block tridiagonal and block pentadiagonal matrices (Q879472)

The authors develop recurrence formulas by using bordering technique for computing a factored sparse approximate inverse for block tridiagonal and block pentadiagonal matrices \(A\). If \(A\) is a symmetric, positive definite matrix or an \(M\)-matrix, then it is guaranteed that the approximate triangular factorization of \(A^{-1}\) exists. The application of the presented algorithms for preconditioning Lyapunov matrix equations is discussed. Furthermore, the methods are used to construct preconditioners for the biharmonic equation discretized by a standard central difference formula. The numerical results show the effectiveness of the new methods. The presented algorithms are well suited for parallel computers.