The SPAI algorithm, a sparse approximate inverse preconditioning technique for large sparse linear systems, proposed by Grote and Huckle [SIAM J. Sci. Comput., 18 (1997), pp. 838–853.], is based on the F-norm minimization and computes a sparse approximate inverse M of a large sparse matrix A adaptively. However, SPAI may be costly to seek the most profitable indices at each loop and M may be in...