The Analytic Solution of Operator Equation of the First Kind

Let W_2~1[a,b]≡W_2~1 = {u(x)| u(x) is absolute continuous real function on [α,b],and u' (x)∈L~2[α,b]}. Set inner product     

The Formal Solution of the First Kind Ⅲ-Posed Operator Equation

In this paper,we discuss the problem for seeking the solution on the firstkind ill—posed operator eguation Au=f with discontinuity of A~(-1) in the spaceW_2~1.Using the regenerating kernel,we introduce the concept of the formal solu-tion of(the eguation) Au=f,and obtain the stable numerical solution from thepartial sum of the formal solution、Therefore,the process using the method ofregularity and quasi-solution for seeking functional minimum to obtain the numerical solution can be omited.     

W22[a,b]空间中的最佳Hermite插值算子

本文介绍具有再生核的函数Hilbere空间W₂²给出了W₂²空间再生核的有限表达式,利用它构造出最佳Hilbere插值逼近算子(H_2nu)(x)的真体表达式,当节点系无限加密时,能够保证(H_2nu)(x)一致收敛于u(x),(H_2nu)(y)一致收敛于u'(x),且每增加一个节点,误差在Sobolev范数意义下单调下降。