Theorems of Stein-Rosenberg Type

Abstract

To obtain a solution of the linear system of equations

$$ A\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {x} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {b} , $$

((1.1))

where A is an n Xn complex matrix, it is often convenient to consider the splitting of A,

$$ A = D - L - U, $$

((1.2))

where D, L, and U are n X n matrices with D nonsingular.