Optimality properties of a square block matrix preconditioner with applications. (15th July 2020) - Axelsson, Owe
Abstract: A preconditioned square block matrix, called PRESB has previously been applied successfully and, for more standard type of problems, have been shown to have eigenvalue bounds in the interval ( 1 ∕ 2, 1 ], which holds uniformly with respect to all parameters involved. Having such fixed bounds enables the use of an inner-product free acceleration method, such as the Chebyshev iterative method. Here it is shown that the method can be applied also for some more general problems, where the spectrum contains outlier eigenvalues larger than unity and that one can apply a polynomially modified version of the Chebyshev method for such problems.