Using the discriminant in a numerically stable symmetric 3 × 3 direct eigenvalue solver

Analytical methods for solving eigenvalue problems involving real symmetric 3 × $$ 3\times matrices are computationally efficient compared to iterative approaches, but not numerically robust when two of the eigenvalues coalesce. Analysis associated characteristic polynomial reveals an alternative form definition discriminant in terms a sum squares which is susceptible numerical difficulties conventional methods. Expressions angle used derived simple combinations matrix invariants and discriminant. The proposed method improves over previously analytical schemes comparable speed with standard method, making it viable alternative.