Given a generalized eigenvalue problem $Ax=\lambda Bx$ for $A, B \in \mathbb{R}^{n \times n}$. Under the assumption that both of $A$ and $B$ are symmetric and one of them is symmetric positive definite, we study some properties of a symmetric version of SVD-QR reduction method and contrast it with Cholesky-QR method. Our study shows the ability of SVD-QR in providing comparable accurate solutions. Beside, for some special problems in this area, the ability of choosing and applying an appropriate version of SVD-QR method shows its flexibility which results in the solutions with less need to apply an iterative refinement.
