An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT...An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.展开更多
Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are ...Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.展开更多
正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)中至关重要的一项技术是信道估计,本文提出一种基于矩阵恢复的OFDM信道估计方法,将连续多个OFDM信号的频域信道构造成一个信道矩阵,由于这个信道矩阵是低秩的,所以可以...正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)中至关重要的一项技术是信道估计,本文提出一种基于矩阵恢复的OFDM信道估计方法,将连续多个OFDM信号的频域信道构造成一个信道矩阵,由于这个信道矩阵是低秩的,所以可以将信道估计问题转换为信道矩阵的加权截断核范数最小化问题,并使用改进的奇异值阈值(Singular Value Thresholding,SVT)算法对信道矩阵进行恢复。仿真结果表明,本文提出的方法和传统信道估计算法相比,使用相同导频数可以获得更高的估计精度,在获得相同估计精度时,消耗导频数更少。与基于压缩感知的信道估计方法相比,本文方法消耗相同数量的导频,但可直接获得高精度的OFDM信道的频域估计。展开更多
文摘An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.
基金Project supported by the Key Laboratory Project of Computational Physics of National Defense Science and Technology of China(Grant No.6142A05180401)the National Key Program for S&T Research and Development of China(Grant Nos.2019YFA0307700 and 2016YFA0401100)the National Natural Science Foundation of China(Grant Nos.11847307,11425414,11504215,11774361,and 11874246).
文摘Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.
文摘正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)中至关重要的一项技术是信道估计,本文提出一种基于矩阵恢复的OFDM信道估计方法,将连续多个OFDM信号的频域信道构造成一个信道矩阵,由于这个信道矩阵是低秩的,所以可以将信道估计问题转换为信道矩阵的加权截断核范数最小化问题,并使用改进的奇异值阈值(Singular Value Thresholding,SVT)算法对信道矩阵进行恢复。仿真结果表明,本文提出的方法和传统信道估计算法相比,使用相同导频数可以获得更高的估计精度,在获得相同估计精度时,消耗导频数更少。与基于压缩感知的信道估计方法相比,本文方法消耗相同数量的导频,但可直接获得高精度的OFDM信道的频域估计。
