Computing error bounds in solving linear systems
J. Schröder · Mathematics of Computation · 1962
I IFI R : C C ! $ I RA ION.A method is presented for computing a vector vO, he calculation of which has the vectors BnvO. This forms an iterative procedure parallel to an approximation procedure. This estimation procedure can be programmed for computers as easily a the approximation procedure. The method theoretically is always successful for some p if the matrix B is irreducible and noncyclic and if the maximal root lambda of B is smaller than 1. Practically, lambda will have to satisfy o e at tronger conditions because one can only calculate with a certain number of digits and one can only perform a certain number of iteration steps. (Author)