求解大规模非对称矩阵特征问题的精化双正交Lanczos算法

We combine Lanczos algorithm with the thought of the refined projection method using QR factorization and propose the refined biothogonalization Lanczos method for computing the desired eigenvalues of large unsymmetric matrix. With low cost of work space and flops the algorithm cures the disease that the Ritz vectors may not converge when the Ritz values converge usingthe Lanczos method. Numerical experiments show our algorithm is considerably more stable and efficient than its counterpart.     

两类新的loop代数及其应用

利用构造的两类特殊 loop代数 ,建立了线性等谱问题 .作为应用 ,求得了著名的 Kd V方程族和 Tu方程族的可积耦合系统 .这种方法可以普遍地应用     

New periodic solutions to a generalized Hirota－Satsuma coupled KdV system

Using expansions in terms of the Jacobi elliptic cosine function and third Jacobi elliptic function, some new periodic solutions to the generalized Hirota－Satsuma coupled KdV system are obtained with the help of the algorithm Mathematica. These periodic solutions are also reduced to the bell-shaped solitary wave solutions and kink-shape solitary solutions. As special cases, we obtain new periodic solution, bell-shaped and kink-shaped solitary solutions to the well-known Hirota－Satsuma equations.     

一个小波函数指数参数变化的分岔现象

研究一个高斯小波函数产生的混沌分岔现象.随着小波函数中指数参数的增加，它的分岔图出现了倍周期分岔，然后出现混沌，经过一段混沌区域后又出现2的幂周期.在整个过程中，正分岔与逆分岔完整地结合在一起.改变小波函数的系数出现一些明显的奇数周期，如3周期、5周期等.绘制Lyapunov指数曲线及映射折射过程，对混沌现象进行研究.将小波函数展开成近似的多项式函数，对近似多项式函数的分岔图进行了分析. 关键词： 混沌 分岔 小波函数     

Two expanding forms of a Lie algebra and their application

With the help of a known Lie algebra,two new high order Lie algebras are constructed.It is remarkable that they have different constructing approaches.The first Lie algebra is constructed by the definition of integrable couplings.the second one by an extension of Lie algebra,Then by making use of Tu scheme,a generalized AKNS hierarchy and another new hierarchy are obtained.As a reduction case of the first hierarchy,a kind of coupled KdV equation is presented.As a reduction case of the second one,a new coupled Schroedinger equation is given.     

基于事件相机的无人机目标跟踪算法

无人机目标跟踪可应用于消防、军事等重要领域,已成为计算机视觉领域热门研究课题之一。现有的无人机目标跟踪算法大多基于传统RGB相机结合深度学习算法, 但此类算法一方面无法避免无人机机体抖动造成的运动模糊, 另一方面因传统RGB相机在低光照或过曝光场景下成像质量较差,难以跟踪目标,为此提出采用无人机搭载DAVIS事件相机的方法进行目标跟踪。设计了基于事件与灰度图的双模态融合跟踪网络,用Vicon运动捕捉系统制作了无人机视角下的目标跟踪Event-APS 28数据集,实现了在复杂光照场景下对目标物的有效跟踪。     

求解大规模Hamilton矩阵特征问题的辛Lanczos算法的误差分析

对求解大规模稀疏Hamilton矩阵特征问题的辛Lanczos算法给出了舍入误差分析.分析表明辛Lanczos算法在无中断时,保Hamilton结构的限制没有破坏非对称Lanczos算法的本质特性.本文还讨论了辛Lanczos算法计算出的辛Lanczos向量的J一正交性的损失与Ritz值收敛的关系.结论正如所料,当某些Ritz值开始收敛时.计算出的辛Lanczos向量的J-正交性损失是必然的.以上结果对辛Lanczos算法的改进具有理论指导意义.