Fredholm第一种积分方程Ax=y的表示定理和一次迭代定理<sup>*</sup>

云天铨

Fredholm第一种积分方程Ax=y的表示定理和一次迭代定理^*

云天铨

华南理工大学工程力学系

基金项目: * 国家自然科学基金资助课题

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出版历程
- 收稿日期: 1988-04-05
- 刊出日期: 1989-07-15

Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y

Yun Tian-quan

Department of Engineering Mechanics, South China University of Technology, Guangzhou

摘要

摘要: 本文给出两个定理.表示定理指出:若具有界L₂核的Fredholm第一种积分方程Ax=y有唯一解,则其中,一次迭代定理指出:可由公式=x₀+g₀A^*(y-Ax₀)一次迭代求得的充分和必要条件是满足下列条件之一:

Abstract: In this paper, two theorems are presented. The representation theorem stales: if the Fredholm integral equation of the first kind Ax=y, with bounded L₂ kernel, has a uniquesolution , Then ,where .The one-iteration theorem states: can be achieved in one iteration by =x₀+g₀A^*(y-Ax₀)if one of the following conditions is satisfied:

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参考文献(15)

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