Experiences with a method for enclosing solutions of systems of equations

In a recent paper the author has demonstrated how to derive inclusions of solutions of systems of equations from hypernorm estimates and a procedure for computing upper bounds for vectors of the type (I − K)−1v, where I denotes the unit matrix, K a nonnegative matrix with spectral radius less than 1 and v a nonnegative vector. s paper one of the resulting methods based on the same information as well-known interval arithmetic methods developed by S.M. Rump is studied. Two algorithms for computing componentwise inclusions, one for solutions of nonlinear problems and one for solutions of linear problems are presented. Comparisons with corresponding algorithms suggested by Rump are carried out for two concrete problems.