Enclosing Solutions of Linear Equations

Jiri Rohn, Georg Rex
1998 SIAM Journal on Numerical Analysis  
It is shown that Rump's method for enclosing solutions of linear equations can be reformulated in an interval-free form and that the underlying inclusion result can be proved by elementary means without using Brouwer's fixed-point theorem. A sufficient condition on Rump's "inflation parameter" ε is given under which finite termination occurs. Also, a more general modified algorithm is studied for which the number of iterations can be expressed by an explicit formula.
doi:10.1137/s0036142996299423 fatcat:vvvvwohw7jap7nhnjabdkekvxi