An algorithm for complex factorization of the bi-periodic Fibonacci and Lucas polynomials

In this paper, we consider the factorization of generalized sequences, by employing a method based on trigonometric identities. The new method is of reduced complexity and represents an improvement compared to existing results. We establish a connection between the bi-periodic Fibonacci and Lucas polynomials and tridiagonal matrices, which exploits the calculation of eigenvalues of associated tridiagonal matrices.