The boundary value problem (BVP) for parameterized singularly perturbed second order nonlinear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivat...The boundary value problem (BVP) for parameterized singularly perturbed second order nonlinear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.展开更多
Given a complete graph with edge-weights satisfying parameterized triangle inequality, we consider the maximum Hamilton path problem and design some approximation algorithms.
For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint ...For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.展开更多
In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticit...In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
In this paper, we consider a parameterized singularly perturbed second order quasilinear boundary value problem. Asymptotic estimates for the solution and its first and second derivatives have been established. The th...In this paper, we consider a parameterized singularly perturbed second order quasilinear boundary value problem. Asymptotic estimates for the solution and its first and second derivatives have been established. The theoretical estimates have been justified by concrete example.展开更多
针对传统运行工况传递路径分析(operational transfer path analysis,简称OTPA)存在的不足,通过理论和试验分析,提出基于Tikhonov正则化方法的OTPA反问题模型。首先,分析Tikhonov正则化方法的理论优势,给出Tikhonov正则化参数选择的依据...针对传统运行工况传递路径分析(operational transfer path analysis,简称OTPA)存在的不足,通过理论和试验分析,提出基于Tikhonov正则化方法的OTPA反问题模型。首先,分析Tikhonov正则化方法的理论优势,给出Tikhonov正则化参数选择的依据,同时调节电机转速获得不同运行工况数据,利用奇异值分解方法研究壳体结构的振动传递路径,分析传统OTPA算法总贡献量误差及路径贡献量估计精度;其次,分析运行工况数据是否满足Picard条件,提出基于Tikhonov正则化方法的OTPA算法,并分析Tikhonov正则化参数对所提出算法的影响。分析结果表明,所提出的方法显著减小了总贡献量和路径贡献量误差以及路径误判现象。该研究可为振动噪声监控与减振降噪提供理论依据。展开更多
Set Packing问题起源于分割问题的应用,是在强约束条件对元素进行划分。在复杂性理论中,此问题是一类重要的NP难问题,被广泛应用于调度、代码优化和生物信息学等领域。特别是在参数计算理论产生后。此问题再次成为研究的热点问题。依据...Set Packing问题起源于分割问题的应用,是在强约束条件对元素进行划分。在复杂性理论中,此问题是一类重要的NP难问题,被广泛应用于调度、代码优化和生物信息学等领域。特别是在参数计算理论产生后。此问题再次成为研究的热点问题。依据所研究问题的差异,本文将Set Packing问题分成5类,并给出了具体的定义。在此基础上,分别介绍了求解这5类问题的相关算法,着重分析和比较了参数算法中所运用的各项技术,并提出了该问题算法研究的一些发展方向。展开更多
文摘The boundary value problem (BVP) for parameterized singularly perturbed second order nonlinear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.
文摘Given a complete graph with edge-weights satisfying parameterized triangle inequality, we consider the maximum Hamilton path problem and design some approximation algorithms.
文摘For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.
文摘In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
文摘In this paper, we consider a parameterized singularly perturbed second order quasilinear boundary value problem. Asymptotic estimates for the solution and its first and second derivatives have been established. The theoretical estimates have been justified by concrete example.
基金Supported by NSFC(11226337,11501525)Science Technology Innovation Talents in Universities of Henan Province(16HASTIT040)+2 种基金Project of Youth Backbone Teachers of Colleges and Universities in Henan Province(2013GGJS-142,2015GGJS-179)ZZIA Innovation Team Fund(2014TD02)Natural Science Foundation of Zhengzhou City(141PQYJS560)
文摘针对传统运行工况传递路径分析(operational transfer path analysis,简称OTPA)存在的不足,通过理论和试验分析,提出基于Tikhonov正则化方法的OTPA反问题模型。首先,分析Tikhonov正则化方法的理论优势,给出Tikhonov正则化参数选择的依据,同时调节电机转速获得不同运行工况数据,利用奇异值分解方法研究壳体结构的振动传递路径,分析传统OTPA算法总贡献量误差及路径贡献量估计精度;其次,分析运行工况数据是否满足Picard条件,提出基于Tikhonov正则化方法的OTPA算法,并分析Tikhonov正则化参数对所提出算法的影响。分析结果表明,所提出的方法显著减小了总贡献量和路径贡献量误差以及路径误判现象。该研究可为振动噪声监控与减振降噪提供理论依据。
