Enhancing Gershgorin-type theorems: Novel approaches to localization of generalized tensor eigenvalues

This paper introduces novel inclusion sets for localizing generalized eigenvalues of tensor pairs. First, we present new Gershgorin-type theorems that define regions in the complex plane, providing greater computational simplicity than existing methods. Second, we develop discs that remove restrictive assumptions, broadening the method's applicability to a wider range of tensors. These proposed sets offer both computational efficiency and tighter eigenvalue bounds than previous techniques. Numerical examples are included to demonstrate the method's superior accuracy and effectiveness.