LOBPCG

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem

$${\displaystyle Ax=\lambda Bx,}$$

for a given pair ${\displaystyle (A,B)}$ of complex Hermitian or real symmetric matrices, where the matrix ${\displaystyle B}$ is also assumed positive-definite.