<FONT face=Verdana>A novel adaptive and iterative training algorithm of least square support vector machine regression (AILSSVR) is presented based on the least square support vector machine regression (LSSVR) and the proof for inverse of an order-reduced matrix is given. Compared to the standard LSSVR

the proposed algorithm takes advantage of the previous training results when learning from a new sample; therefore

it can obtain a new learning machine efficiently. Numerical simulations demonstrate that AILSSVR can adaptively decide the number of support vectors and preserve the sparse property of support vectors in QP training methods. Under the similar regression accuracy

AILSSVR can speed up the learning process remarkably.