def METHOD_NAME(self):
    A_inv = self._diag_tensor.inverse()  # This is fine since it's a DiagLinearOperator
    U = self._linear_op.root
    V = self._linear_op.root.mT
    C = ConstantDiagLinearOperator(torch.ones(*V.batch_shape, 1, device=V.device, dtype=V.dtype), V.shape[-2])
    cap_mat = to_dense(C + V.matmul(A_inv.matmul(U)))
    METHOD_NAME = psd_safe_cholesky(cap_mat)
    return METHOD_NAME