W_2~1（B）空间中的最佳逼近及半直线上积分方程数值解

THE OPTIMAL APPROXIMATION AND THE NUMERICAL SOLUTIONS FOR INTEGRAL EQUATIONS ON THE HALF￣LINE IN THE SPACE W_2￣1 (B)

讨论了Ｗ＾１２（Ｂ）空间中线性算子的最佳逼近及半直线上积分方程的近似解。得到最佳逼近算子的表达式。在仅知方程右端项的有限个离散值时给出了方程近似解的表达式，并证明误差序列在Ｗ＾１２（Ｂ）范数意义下单调下降。

The optimal approximation of linear operator and the approximate solutions for integral equations on the half--line are discussed in the space W; (B). The representation of optimal approximation is obtained. The approximate solutions are given, and the monotonically decreasing property of error sequence is proved.