关于绝对连续函数的黎曼-斯蒂尔切斯积分的近似计算

Approximation of the Riemann-Stieltjes Integral with Absolutely Continuous Integrand

研究了闭区间[a,b]上的黎曼-斯蒂尔切斯(R-S)积分∫ab f(x)d u(x),对于函数f(x)和u(x)皆为绝对连续函数的情形得到了近似计算的求积公式及其误差估计,并将结果应用于富里埃正弦变换和富里埃余弦变换的近似计算及其误差分析.

As it is well-known to us, Riemann-Stieltjes integral is an important generalization for Riemann integral. Here our purpose is to investigate the numerical method and its analysis of error of R-S integral under certain condition of integral,such as absolutely continous function and its derivative of first or second order with Lp integrability.Finally, we apply the results to get numerical analyis for Fourier Sine and Cosine transforms of some function.