奇异积分的有限积分及其截断Hermite插值逼近

THE APPROXIMATION OF SINGULAR INTEGRALS BY FINITE-INTEGRATION AN HERMITE INTERPOLATORY

本文讨论具有形式的Ｃａｕｃｈｙ主值积分．文中定义了奇异积分对于给定点集的有限积分，并导出了上述Ｃａｕｃｈｙ主值积分用有限积分表示的公式。在上述基础上，本文给出了一种对上述Ｃａｕｃｈｙ主值积分的简便而有效的截断Ｈｅｒｍｉｔｅ插值逼近方法，并给出了其误差估计和收敛性定理．

In this paper,the cauchy principal value integrals of the form is discussed.The finite-pair intrgration of singlar integrals is defined,and the formula for the Cauchy principal value integrals by finite-part integration is gerived. On the basis of the above, We get a simple amd effectove approximate metyhod by Hermite interpolatory is edscribed, and the its error estimate and the convergence theorem are obtained.