Validated Solution of Large Linear Systems

Abstract

some new methods will be presented for computiong verified inclusionsof the solution of large linear systems. The matrix of the linearsystem is typically of sparse or band structure. There are no prerequisitesfor the matrix, such as being M-matrix, symmetric, positive definiteor diagonally dominant. For general band matrices of lower, upperbandwidth p, q of dimension n the computing time is n(pq + p^2 +q^2). Examples with up to 1.000.000 unknowns will be presented.