Error estimates for the solution of linear algebraic systems

In thi s paper bounds for th e e rror of a computed inverse of a matrix a re developed. These are th e n app lied to th e solution of a s in gle sys tem. Methods for improving th e app rox imate inverse are th e n discussed with so me observa tions on th e dange rs involved in the ir pract ical use on a co mpute r a nd so me sa feguard s a re indica ted. So me compute r p rogra ms for matrix invers ion are th en evaluated by means of th e bound s deve loped.