Spectral Properties of Numerical Differentiation
Maxim Dvornikov (University of Jyväskylä and IZMIRAN)
我们研究具有任意节点数的网格中给出的函数的数值分化公式。 我们调查计算第一个和第二个衍生物的公式中的无限点数的情况。 获得相应的重量系数序列的光谱。 我们检查奇数点给出的函数的第一个导数计算,并分析有限和无限多节点情况下权重系数序列的光谱。 我们得出第一个导数的片面近似值,并检查其光谱特性。
We study the numerical differentiation formulae for functions given in grids with arbitrary number of nodes. We investigate the case of the infinite number of points in the formulae for the calculation of the first and the second derivatives. The spectra of the corresponding weight coefficients sequences are obtained. We examine the first derivative calculation of a function given in odd-number points and analyze the spectra of the weight coefficients sequences in the cases of both finite and in...