New Root-Location Theorems for Partitioned Matrices
Joel L. Brenner · SIAM Journal on Applied Mathematics · 1968
In solving systems of linear equations by iteration methods, an advance guarantee is sometimes needed that the iteration will converge. Such a guarantee is available from one or another of the class of theorems known as root-location theorems, or Gershgorin-type theorems. In an unpublished report [2], I have given methods for discovering such theorems and for finding counterexamples to unfounded conjectures. In the present paper, several new root-location theorems are given.