数值算法

Contain a "scientific and engineering numerical calculation method," a book full source code.

内容包含了《科学与工程数值计算算法》一书中全部的源代码。

A numerical calculation program is written up for the various solution methods in this paper and the program is being used in various aspects of inverse problem of environmental hydraulics, including inverse problem in reverse process of one-dimensional unstable diffusion, inverse problem in reverse process of convection-diffusion, inverse problem for the dispersion coefficient in water quality model, The inverse problem of coefficient identification for nonlinear Boussinesq equation, parameter identification inverse problem for water quality model, the inversion of parameter of BOD-DO water model, the inverse problem of the source of convection-diffusion, identification of the steady-state permeability for two dimensional isotropic medium, two-dimensional steady inverse problem of convection-diffusion and parameter identification inverse problem for two-dimensional parabolic equation, etc.

对本文提出的各种算法，编制了数值计算程序，并把它应用于环境水力学反问题诸多领域，包括污染物一维非恒定扩散逆过程反问题，对流扩散方程逆过程反问题，河流水质纵向弥散系数反问题，非线性Boussinesq方程反问题，河流水质多参数识别反问题，BOD-DO水质模型参数反演问题，对流—扩散方程源项反问题及二维恒定各向同性介质渗透系数反问题，二维定常对流——扩散方程及二维抛物型方程参数控制反问题等。

Radau collocation method has high accuracy and good numerical stability.

该算法具有计算精度高、数值稳定性好等特点。

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

Finally, the computational results of the examples show the feasibility and efficiency of the algorithm.

并通过数值算例的计算结果说明了该算法的可行性和有效性。

By means of integralequation methods creatively along with other modern mathematical theories,this paperfocuses on finding solvability conditions and conditional well-posedness(especiallyconditional stability),constructing stabilized algorithms,and carrying throughnumerical simulation.

本文创造性地应用积分方程方法，借助现代数学手段，着重研究这些问题的可解性条件、条件适定性，构造稳定化算法，并进行数值模拟。

Finally, the numerical results show this class of conjugate gradient methods is very efficient.

然后证明三种新算法在强Wolfe线搜索下的全局收敛性，数值验证表明这类共轭梯度法是比较有效的。

Combined CD method and a new conjugate gradient method given by Liu.Y, Storey. C, the second class of nonlinear conjugate gradient method is proposed, which not only has descent property, but also is proved global convergence with the general Wolfe line search. Finally, the numerical results show this class of conjugate gradient methods is very efficient.

第二类算法是结合CD法和Liu.Y， Storey.C提出的新共轭梯度法，提出一类新的非线性共轭梯度法，新方法不但具有下降性质，而且在推广的Wolfe线搜索下是全局收敛的，最后进行了数值验证。

Order Hilbert ill-conditioned linear equations were solved, and the relative error was less than 0.45%. Numerical experiments verified that the method was efficient compared with the efficient methods used commonly nowadays. Numerical experiments results showed that the conjugate vector base method was suited for solving large-scale ill-conditioned linear equations with fast convergence and high precision.

通过对5000阶的Hilbert方程组进行求解，结果的相对误差小于0.45%，并与当前普遍使用有效的方法进行了比较，数值实验结果表明，该算法适合求解大型病态线性方程组，且具有快速收敛，精度较高的特性。

Experimental results indicate that the IPSO is robust and efficient in solving nonlinear constrained optimization problems.

对比数值实验结果表明，该算法能够有效、稳定地求解非线性约束优化问题。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。