为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其...为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其相关应用研究进行对比分析。结果表明,在谱聚类的应用上,通过降低核心步骤SVD(Singular Value Decomposition)的复杂度,使优化后的算法与原始谱聚类算法的精度相近,但大大缩短了运行时间,在1200维的数据下计算速度相较原算法快了10倍以上。同时,该方法应用于图像压缩领域,能有效地提高原有算法的运行效率,在精度不变的情况下,运行效率得到了1~5倍的提升。展开更多
Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the ...Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to展开更多
文摘为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其相关应用研究进行对比分析。结果表明,在谱聚类的应用上,通过降低核心步骤SVD(Singular Value Decomposition)的复杂度,使优化后的算法与原始谱聚类算法的精度相近,但大大缩短了运行时间,在1200维的数据下计算速度相较原算法快了10倍以上。同时,该方法应用于图像压缩领域,能有效地提高原有算法的运行效率,在精度不变的情况下,运行效率得到了1~5倍的提升。
文摘Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to
