A Study on Piecewise Polynomial Smooth Approximation to the Plus Function

In smooth support vector machine (SSVM), the plus function must be approximated by some smooth function, and the approximate error will affect the classification ability. This paper studies the smooth approximation to the plus function by piecewise polynomials. First, some standard piecewise polynomial smooth approximation problems are formulated. Then, the existence and uniqueness of solution for these problems are proved and the analytic solutions are achieved. The comparison between the results in this paper and the previous ones shows that the piecewise polynomial functions in this paper achieve better approximation to the plus function