Locally Optimal Block Preconditioned Conjugate Gradient is a matrix-free method for finding the largest eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem A x = λ B x, {\displaystyle Ax=\lambda Bx,} for a given pair {\displaystyle } of complex Hermitian or real symmetric matrices, where the matrix B {\displaystyle B} is also assumed positive-definite. Wikipedia