L^1-space中基于强收敛意义下函数最优逼近的VSOW法研究

Researches on Optimal Approximation of Functions in L^1-space by Using the VSOW Method Based on Strong Convergence

指出L1-space中任意一个闭区间[a,b]上的连续函数f(x),都可用[a,b]上的线性无关的连续函数族{gi(x)}的线性组合来逼近。并在强收敛意义下证明了这种最优逼近式的存在性、唯一性问题,进一步地,给出了确定这种最优逼近式的VSOW方法,并揭示了运用这种VSOW法在L1-space中所确定的最优逼近式的敛散性问题。

This paper discussed L^1-space＇s optimal approximation in detail by talking over the approach of VSOW method based on the Weierstrass theorem and applying it to L^1-space,and thus solves the existence and unique of L^1-space＇s best-fit polynomial approximation is solved. Furthermore,it also proves the convergence of VSOW method is proved when it is applied to the solution of L^1-space＇s optimal approximation.