This volume contains 22 papers presented at the Kiel Seminar in 1992. The Kiel Seminars are well known, and cover special areas in numerical methods for partial differential equations, numerical linear algebra, numerical methods for integral equations and related areas. The papers cover a broad range of topics from mathematical theory to practical applications of incomplete decompositions as smoothers in multi-grid methods, as preconditioners for conjugate gradient-type methods and the use of ILU for systems of partial differential equations.