Fredholm第一类积分方程数值解的可靠性

Reliability of the Numerical Solution to the Fredholm Integral Equation of the First Kind

讨论了一个Ｆｒｅｄｈｏｌｍ第一类积分方程数值解的可靠性问题．对于Ｆａｂｒｙ－Ｐｅｒｏｔ干涉反演光谱学中的第一类积分方程，当Δσ＝２／ｘ，Δｘ＝２／σ，且等距取样点数为一个适当的奇数时，虽然采用最简单的矩形求积公式可离散得一个稳定的线性方程组，但是该方程组的解却不是原积分方程的解，换句话说，该稳定的数值解是不可靠的．

This paper discusses the reliability of the numerical solution to a Fredholm integral equation of the first kind. Although a stable system of linear equations can be obtained from the integral equation of the first kind in the Fabry Perot inverse interfe rence spectroscopy, by using the simplest rectangle formula, in the case Δσ=2/x, Δx=2/σ and the number of equally spaced sampling points being a suitable odd one, its solution is not the solution to the original integral equation. That is to say, the stable numerical solution is not reliable.