查询词典 general algebraic equation

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

One is the existence problem of real symmetric solutions of the general algebraic Riccati equation , the other is the optimal output feedback problem under the LQ index.

此外，本文还涉及了两个控制理论界多年来受到广泛注意和研究的难题；其一是一般代数Riccati方程的实对称镇定解的存在性问题：其二是线性二次型指标下的直接最优输出反馈问题。

So, in this paper, a circular cavity witha large radius is used to replace the straight boundary of thehalf space, then the half space problem can be changed tothe scattering problem of two circular cavities to the steadyincident P-wave . Having the aid of the mature cylinderfunction theory, the general solutions of the wave functionscan be given, and an infinite linear algebraic equations ofthe unknown coefficients in the wave functions can be gottenwith the boundary conditions and the Fourier complex seriesexpansion technology, the infinite linear algebraic equationscan be approximately solved by the finite trunction withsatisfying some definite precision, at the basis of thissolution of the equation, the variations and the lay-outs ofthe DSCF at the circular cavity boundary vs. the differentincident angles, the different embedded depths of thecircular cavity as well as the different dimensionless wavenumber of the incident P-wave.

为此，本文采用一个半径很大的圆孔来代替半空间的直边界，将该半空间问题转化为一无限大空间中两个圆孔对稳态P波的共同散射问题，借助于成熟的柱函数理论，通过写出问题波函数的一般形式解，利用问题的边界条件，并采用复数傅立叶级数展开技术将其化为一个仅包含问题波函数中未知系数的一无穷线性代数方程组，在满足一定计算精度的前提下，通过有限项截断进行近似求解，进而讨论了圆孔边界处的动应力集中系数随不同入射角、不同的圆孔掩埋深度、入射波的不同无量纲波数以及介质的泊松比变化和分布情况。

According to the analysis of general sm all signal stability m ethod,the conclusion can be drawn that the algebraic- equation constraints and the coupling between state variables are responsible for the complex dynam ic behavior of the systems.

文中首先对研究系统稳定问题的小扰动方法进行了分析，认为非线性动力系统的代数方程约束和各状态量之间的耦合关系是造成系统动态特性十分复杂的重要原因，进而利用同伦函数的概念给出了一种确定线性化系统中特征值与状态变量对应关系的方法。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。