A Note on the Newoton Iteration for the Algebraic Eigenvalue Problem
Maria Célia Santos · SIAM Journal on Matrix Analysis and Applications · 1988
This paper considers the Newton iteration for the algebraic eigenvalue problem $( \lambda I - A )x = 0,\Phi ( x ) = 1$, where $\Phi $ is a convex forming function that is not necessarily differentiable. The role usually played by the Fréchet or Gateaux derivatives will be performed by a choice of subgradients of $\Phi $. Under very mild conditions on $\Phi $, the local and Q-superlinear convergence of this extended Newton iteration are proved. The stability of the process is also investigated.