矩阵补全特别是具有结构化矩阵的低秩矩阵补全得到国内外学者的广泛关注。基于此,笔者在详细叙述hankel矩阵补全的交替方向算法(Alternating Direction Method ADM)的基础上研究此算法在我国航空货运量预测中的应用,以1995-2010年我国...矩阵补全特别是具有结构化矩阵的低秩矩阵补全得到国内外学者的广泛关注。基于此,笔者在详细叙述hankel矩阵补全的交替方向算法(Alternating Direction Method ADM)的基础上研究此算法在我国航空货运量预测中的应用,以1995-2010年我国航空货运量的统计数据为基础,利用Matlab软件求解相应Hankel矩阵补全问题可得我国航空货运量逐年预测值。通过预测误差分析可知,此方法可应用于短期内预测我国的航空货运量,为我国航空货运市场的中长期调控提供有效的理论依据。展开更多
We study the Fredholm integro-differential equationby the wavelet method. Here (x) is the unknown function to be found, k(y) isa convolution kernel and g(x) is a given function. Following the idea in [7], theequation ...We study the Fredholm integro-differential equationby the wavelet method. Here (x) is the unknown function to be found, k(y) isa convolution kernel and g(x) is a given function. Following the idea in [7], theequation is discretized with respect to two different wavelet bases. We then havetwo different linear systems. One of them is a Toeplitz-Hankel system of the form(Hn + Tn)x = b where Tn is a Toeplitz matrix and Hn is a Hankel matrix. Theother one is a system (Bn+ Cn)y= d with condition number K = O(1) after adiagonal scaling. By using the preconditioned conjugate gradient (PCG) methodwith the fast wavelet transform (FWT) and the fast iterative Toeplitz solver, wecan solve the systems in O(nlog n) operations.展开更多
文摘矩阵补全特别是具有结构化矩阵的低秩矩阵补全得到国内外学者的广泛关注。基于此,笔者在详细叙述hankel矩阵补全的交替方向算法(Alternating Direction Method ADM)的基础上研究此算法在我国航空货运量预测中的应用,以1995-2010年我国航空货运量的统计数据为基础,利用Matlab软件求解相应Hankel矩阵补全问题可得我国航空货运量逐年预测值。通过预测误差分析可知,此方法可应用于短期内预测我国的航空货运量,为我国航空货运市场的中长期调控提供有效的理论依据。
文摘We study the Fredholm integro-differential equationby the wavelet method. Here (x) is the unknown function to be found, k(y) isa convolution kernel and g(x) is a given function. Following the idea in [7], theequation is discretized with respect to two different wavelet bases. We then havetwo different linear systems. One of them is a Toeplitz-Hankel system of the form(Hn + Tn)x = b where Tn is a Toeplitz matrix and Hn is a Hankel matrix. Theother one is a system (Bn+ Cn)y= d with condition number K = O(1) after adiagonal scaling. By using the preconditioned conjugate gradient (PCG) methodwith the fast wavelet transform (FWT) and the fast iterative Toeplitz solver, wecan solve the systems in O(nlog n) operations.
