When soloving the linear equation $x=Ax+b$ (where $x$ is an unknown vector, $A$ is a matrix, and $b$ is a constant vector), one often use the follow iteration:
$x_{k+1}=Ax_k +b$.
Does the above $x_k$ is convergent to $x$ when the spectral radius of $A$ is less than 1? If yes, would you give a reason. Thanks!