Approximate inverses of multidiagonal matrices and application to the block PCG method (Q1893942)

The authors consider the \(p\)-order truncated elimination to compute approximate inverse matrices of diagonally dominant matrices. For \(p\) a positive integer, the \(p\)-order truncated elimination neglects all the increments of order \(S\) when \(S > p\) in the process of the elimination which results in the \(p\)-order approximate inverse matrix for a multidiagonal band matrix. This method is applied to block preconditioned conjugate gradient method calculations. Numerical examples are given to show the good behavior of the method.