Diagonal Dominance with Strict Constraint

For the traditional diagonal dominance algorithms unconstrained the non-diagonal elements, a strict constraint of diagonal dominance is proposed in the paper. Contrary to the normal definition, the novel definition of strict diagonal dominance restricts the max non-diagonal elements, and the definition of strict Gershgorin discs is also discussed. To achieve diagonal dominance the compensating matrix search algorithm based on trial and error is introduced in the paper. Example of compensating search algorithm is applied to support the proposed method, and the results obtained are comparable with normal method. It gives a novel way to define the diagonal dominance.