Iterative methods for bounding the inverse of a matrix (A survey)


Miodrag S. Petković




The aim of this paper is to give a survey of iterative methods for bounding the inverse of a point, or interval matrix. These methods are based on the generalized Schulz’s method and developed in interval arithmetic.. The interest in bounding roundoff errors in matrix computations has come from the impossibility of exact representation of elements of matrices in those cases when numbers are represented in the computer by strings of bits of finite length or elements were experimentally determined by measurement which leads to the uncertainty in initial data. A posed problem can be usefully solved by interval analysis, a new powerful tool of applied mathematics. A detailed study of the basic inclusion method and its modifications, including the convergence features, conditions for a safe convergence, the monotonicity property, the choice of initial inclusion matrices and a number of remarks concerning a. practical realization, were presented. A special attention is devoted to the construction of efficient, methods for the inclusion of the inverse of a matrix.