The inverse-free extreme learning machine (ELM) algorithm proposed in  was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of a Hermitian matrix. Before that recursive algorithm was applied in , its improved version had been utilized in previous literatures , . Accordingly from the improved recursive algorithm , , several efficient inverse-free algorithms for ELM were proposed in  to reduce the computational complexity. In this paper, we propose two inverse-free algorithms for ELM with Tikhonov regularization, which can increase multiple hidden nodes in an iteration. On the other hand, we also propose two efficient decremental learning algorithms for ELM with Tikhonov regularization, which can remove multiple redundant nodes in an iteration.