Before revision:  Mathematically, SP-BFGS provides a means of incrementally updating the new inverse Hessian approximation with a controlled amount of bias towards the previous inverse Hessian approximation . Practically speaking, this can be used to help replace the overwriting nature of the  BFGS update with an averaging nature that resists the destructive effects of noise .
After revision:  Mathematically, SP-BFGS provides a means of incrementally updating the new inverse Hessian approximation with a controlled amount of bias towards the previous inverse Hessian approximation , which allows one to replace the overwriting nature of the BFGS update with an averaging nature that resists the destructive effects of noise .