In Algorithm 2, the Lanczos algorithm is presented as an example of the diagonalization method, but other diagonalization methods (such as the Davidson algorithm or the Jacobi-Davidson algorithm) could also be used. The algorithm we presented can be transformed into other diagonalization methods by applying different form of the transformation function T (x) specifically. Similarly, the following mixed-precision optimization is introduced with the Lanczos algorithm, but also can be applied for other diagonalization methods. procedure Diagonalization: