讨论了共轭线性算子对应于线性算子的一系列重要性质，并且研究了线性算子与共轭线性算子的一些关系。
A series of important properties of these operators are obtained, some relationships between conjugate linear operators and linear ones are also discussed.
无约束优化问题的共轭梯度路径构造的思想启迪我们用其来解带线性等式约束和有界变量约束的优化问题。
The idea of conjugate gradient path in unconstrained optimization irradiates us to use this method for solving the linear equality optimization subject to bounds on variables.
本文用分片线性元离散椭圆型问题。用预处理共轭梯度法求解有限元方程。
In this paper, the elliptic problems are discreted by linear elements, the finite element system are solved by PCG method.
利用DC规划共轭对偶的思想，讨论解型线性双层规划的共轭对偶规划及其对偶性质。
Then using the thought of the surrogate dual of DC programming, the surrogate dual of bilevel linear programming and the duality properties are given.
本文论证了非线性耦合前向波的位相复共轭特性。
In this paper, the phase conjugate nature of the nonlinear coupling forward wave has been demonstrated.
本文讨论了贝塔分布共轭于二项分布的决策模型下的二行动线性决策问题的抽样信息期望值的计算公式。
In this paper we discuss the counting formula of the expected value of sampling information for linear decision problem on two actions under the Be - b model.
它在理论上是多项式算法，并可以从任意点启动，可以应用共轭梯度方法有效地求解大规模线性不等式组问题。
SDNM is a polynomial time algorithm with the Newtons method, so that SDNM can solve large-scale linear inequalities.
本文介绍了相位共轭光学的基本概念，综述了产生相位共轭波的各种非线性光学技术，并讨论了它们之间的关系。
The fundamental concepts of phase conjugate optics are described. Various nonlinear optical techniques which generate phase conjugate wave are summarized and the relations between them are discussed.
本文介绍一种沿曲线方向线性搜索的算法，这种算法概括了梯度法、共轭梯度法以及它们的改进格式。
This paper introduces a curvilinear line searching technique, which possesses all the meris of the gradient method, the conjugate gradient method and some of their refined types.
本文首次用一种改进的共轭算子法研究了六维非线性系统的三阶规范形以及所用的非线性变换。
An improved adjoint operator method is employed to compute the third order normal form of six dimensional nonlinear dynamical systems and the associated nonlinear transformation for the first time.
提出一种用非线性晶体的相位共轭特性记录扫描全息图的方法。
A method of recording a scanning hologram with the phase conjugate property of nonlinear crystal is presented.
稳定化双共轭梯度法用于求解稀疏线性方程组，可调节参数的修正迭代法用于求解非线性代数方程组。
Linear equations of sparse matrix are solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations are solved by parameter-regulated iterative procedures.
该文提出一种无约束优化非线性共轭梯度法，证明了精确线性搜索下的全局收敛性。
The paper presents a nonlinear conjugate gradient method for unconstrained optimization problem, and proves its global convergence under exact line searches.
该方法利用最大似然准则建立目标函数，同时利用非线性共轭梯度法来优化求解目标函数。
The objective function was established based on the maximum likelihood rule, which was solved by nonlinear conjugate gradient method.
由于向列相液晶大的非线性系数，使得利用向列相液晶产生光学相位共轭波称为可能。
Nematic liquid crystal has a large non-linear coefficient, so it is possible to produce optical phase conjugation (OPC) wave in right condition.
本文研究了解决大型稀疏对称正定线性方程组的一类预条件共轭梯度法。
This paper is investigated a preconditioned conjugate gradient method in solving a linear algebraic system of large sparse symmetric and positive equations.
分别利用了共轭函数法与直接配置和非线性规划方法对异面最优变轨问题进行了求解。
Adjoint function algorithms and direct collocation and nonlinear programming methods are applied to resolve the non-coplanar optimal orbit transfers problem.
主要从事环境微量污染物检测方法及污染机理研究，非线性光学相位共轭技术研究。
Main interests are research on detection methods of trace pollutants, mechanism of environmental pollution and nonlinear optical phase conjugation.
利用优化问题的非线性共轭梯度法与混沌优化方法相结合，提出了一种新的混合优化算法。
A new hybrid algorithm which combines the chaos optimization method and the nonlinear conjugate gradient method approach having an effective convergence property is proposed.
梯度法对许多非线性问题均具有较好的性能，计算目标函数可以使用新的共轭变量法，有望显著提高寻优效率。
Generally, to nonlinear problem, gradient-based method is faster than simple method, and may improve efficiency due to using conjugate variables to calculate object function value.
与其他量子力学计算结果比较，表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用。
Compared with other quantum calculations, DLA method appears to provide an effective method for the calculation of the hyperpolarizability of conjugated organic molecules.
超支化共轭聚合物由子其所具有的良好的非线性光学特性，在功能高分子领域具有广泛的应用前景。
Based on the excellent nonlinear optical properties of hyperbranched conjugated polymer, those polymers are attracting more and more attention as functional polymer materials.
在一般双共轭梯度法的基础上，本文利用广义变分原理对内积进行了重新定义，使双共轭梯度法求解复线性方程组更为有效。
Based on biconjugate gradient method, we redefine inner products using general variation principle, which can make complex linear equations solving have high-performance.
该分子具有大的TPA截面是起源于该分子的刚性平面共轭结构所固有的线性吸收特性和TPA共振增强；
The large TPA cross section may result from the intensive linear absorbance of the molecule due to its conjugate rigid plane structure, and the two-photon resonance excitation condition.
非线性光学相位共轭技术可用于很多光学领域。
Nonlinear optical phase conjugation technology can be used in adaptive optics and optical information processing.
分子共平面，共轭作用强，对增大二阶光学非线性有利。
Coplanar molecules having stronger conjugation effects facilitate the nonlinear second-order optical susceptibilities too.
本文对该算法中的线搜索进行了推广，提出了一种新的非线性共轭梯度算法并证明了其全局收敛性。
This paper presents a wide line search and gives a new conjugate gradient method, with global convergence.
擅长的领域包括：共轭聚合物，纳米晶，超快脉冲激光器，非线性光学，光与物质的相互作用，面向对象程序设计等。
His interests include conjugated polymers, nanocrystals, ultrafast pulsed lasers, nonlinear optics, light-matter interactions, and object-oriented programming.
共轭方向算法是非线性最优化理论中一类重要的算法，确定共轭向量是共轭方向算法的关键。
Conjugate direction algorithm is an important algorithm in the theory of optimization. Determining conjugate vectors is a key in conjugate direction algorithm.
本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。
In this paper, we show that the isometry between the unit spheres of certain normed space and its dual space can be extended to a real linear isometry on the whole space.
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