Due to the convergence of cg method is strongly dependent on the condition number of the hessian , the inexact newton method with cg subiterations will be powerful if these cg subiterations are replaced by preconditioned cg subiterations with suitable preconditioner 由于cg法的收敛状态强烈的依赖于海色阵的条件数，所以用条件预优共轭梯度法( pcg )替代cg法会得到更好的效果。
The condition numbers of the jacobian matrix are analyzed to judge velocity transfer performance and force transfer performance between joint space and working space . the three dimensions drawings are drew by matlab to make analysis visual 通过分析雅克比矩阵的条件数来判断关节空间和目标空间的速度传递性和力传递性，利用matlab工具软件进行具体计算，并画出性能的三维图形来使分析可视化。
The traditional methods are to solve the linear algebra equations directly , based on matrix factorization such as lu decomposition . with this kind of methods , the " true " solution can be derived if there is no consideration of the round error 解线性代数方程组的传统方法是利用lu分解等直接求解，虽然传统方法具有理论上直接得到真解的优点，但当系数矩阵条件数很大时，存在严重的稳定性问题。
In the mql module , aim phrase and condition phrase are picked up , and are translated into query aim and query condition . during the translation , correlative contexts are added into entity array , query aim array , query condition array , then mql is produced 再将每一种类型的目标短语和条件短语转化为相应的查询目标和查询条件,填充相关的实体数组、查询目标数组、查询条件数组等,生成完备的中间语言。
The backward error and the structured backward error of the approximate solution are the criteria to judge the stability and the strong stability of the numerical algorithm . condition number is a measure of the sensitivity to the approximate solution for the perturbation of original date 近似解的最佳向后误差和最佳结构向后误差的数值分别是判别算法的稳定性和强稳定性的标准，而条件数则是反映数值问题的解对于该问题数据扰动的敏感程度。
According to rice ' s idea , rice condition numbers for these subspaces are defined by applying perturbation expansions of orthogonal projection operators . the expressions of the rice condition numbers and the first - order perturbation estimations for these subspaces are derived . compared with sun ' s approach , the rice condition numbers are independent of the choices of basis 在子空间基底扰动展开的基础上，基于rice的想法，运用正交投影算子与空间基底选取无关的特性，改进了前人所定义的子空间和子空间对的条件数，并得到了这些rice条件数的具体表达式。
As the perturbation analysis , we make some results on the singular linear equations " condition number concerned with the generalized inverse at , s , ( 2 ) which extend the results on the nonsingular linear equations " condition number , then we give the perturbation bound for the solutions of ep linear equations 在奇异线性方程组解的扰动分析方面，我们首先从最具有代表性的广义逆a _ ( ts ) ~ ( 2 )着手，建立了有关求解奇异线性方程组的条件数的表达式，从而推广了非奇异线性方程组的条件数的一些结果，然后我们对ep线性方程组的广义逆解的相对扰动误差界给出一个估计式。
First , the concept of physical model of the solution space , jacobian and force condition are presented . the isotropy indices of 3 - axis f / t sensor of the platform structure and discoupling structure are studied , and the law of the indices following the changing of structure parameters is summarized 首先介绍了空间模型理论与雅可比矩阵及条件数的概念，分析了三维力传感器在平台式结构和解耦结构情况下的力各项同性性能，总结了两种情况下的力各向同性性能随参数的变化规律。
It is proven that these modified dual algorithms still have the same convergence results as those of the conceptional dual algorithms in chapter 2 and chapter 3 . secondly , a dual algorithm is constructed for general constrained nonlinear programming problems and the local convergence theorem is established accordingly . the condition number of modified lagrange function ' s hessian is estimated , which also depends on the penalty parameter 证明这些修正的对偶算法仍具有同前两章的概念性对偶算法相同的收敛性结果，我们还进一步构造了一般约束非线性规划问题的对偶算法，建立了相应的局部收敛理论，最后估计了修正lagrange函数的hesse阵的条件数，它同样依赖于罚参数。
A new form of parallel robot based on 6 - pts mechanism was presented , and its kinematics analysis was given , including displacement analysis , velocity analysis and acceleration analysis . on the base of inverse displacement model , analyzed its workspace and discussed structural parameter ' s effect on workspace , and developed the kinematics simulation software using vc + + and opengl . finally , optimized its structural parameters with genetic algorithms 首先对该种并联机器人的位移、速度和加速度进行了分析和数据仿真，然后，对工作空间的各截面进行了分析，并讨论了结构参数对工作空间的影响，在运动学反解模型的基础上，利用vc + +和opengl开发了6pts并联机器人运动学可视化仿真平台，最后运用遗传算法对结构参数进行了优化设计，以使机构的雅可比矩阵的条件数取得尽可能小的值。
