Factored sparse approximate inverse of block tridiagonal and block pentadiagonal matricies

This paper is concerned with approaches to compute a factored sparse approximate inverse for block tridiagonal and block pentadiagonal matrices. Recurrence formulas are developed for computing sparse approximate inverse factors of these matrices using bordering technique. Resulting factored sparse approximate inverse is used as a preconditioner for the conjugate gradient method (PCG). As an application these formulas are simplified for computing the preconditioner for solving Lyapanuv matrix equations by PCG method. Numerical experiments on linear system, arising from discretization of partial differential equations are presented.