查询词典 hessian matrix

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

The method for constructing LDPCC code includes encoder and decoder. Operational steps include as following: determining parameters of checkout matrix HQT of group code of permutation unit matrix LDPC; constructing checkout matrix HQT of group code of permutation unit matrix LDPC; constructing checkout polynomial matrix HT of LDPCC code; exporting generated matrix G of LDPCC code.

一种LDPCC码的构造方法，包括编、译码器，运行的步骤包括：初始化的步骤；确定一个置换单位矩阵LDPC分组码的校验阵HQT的参数的步骤；构造置换单位矩阵LDPC码校验阵HQT的步骤；构造LDPCC码的校验多项式矩阵HT的步骤；导出LDPCC码的生成矩阵G的步骤。

The method according to claim 6, for manufacturing a blade wherein a part external to the shell comprises a blade rooting part having at least one attachment bar, in which an end portion for linkage to a hub of said rotor is fitted with a laminate attachment, also comprising thermoplastic composite, and extending said at least one spar bar housed in the shell, the method further comprising the step of producing the elementary piece comprising the at least one spar by producing each attachment bar and the spar bar in the form of a strip of continuous and unidirectional reinforcing fibres which are agglomerated by said thermoplastic matrix, obtained by pultrusion at a melting temperature of the matrix, of several plies of continuous and unidirectional fibres which are agglomerated by said matrix, and, if said rooting part comprises at least two attachment bars, each one of which respectively extends one spar bar, in superimposing parts of corresponding strips forming the spar part housed in the shell, with interposition of at least one ply of continuous and unidirectional fibres which are agglomerated by said matrix between the adjacent superimposed strip parts, and fitting a removable tool, in the shape of a wedge, between parts held spaced from each other of two neighbouring strips, to form two attachment bars of the rooting part, then arranging the strips in a mould, and inserting each linkage end portion of a pultruded strip between two laminate elements of the attachment, to superimpose all the laminate elements of the attachment, closing the mould and compacting its contents under pressure and at a melting temperature of said thermoplastic matrix, and solidifying the matrix by cooling to rigidify the spar thus obtained with the laminate attachment solidly attached to its rooting part.

该方法根据索赔六，制造业刀片其中的一部分，罐壳外部包括一个叶片生根的一部分，拥有至少一个实习酒吧，在其中一结束部分为联系枢纽的说，转子是带有附件的层压板，也包括热塑性复合材料，并延长说，至少有一石酒吧住在蚬壳公司，进一步组成的方法步骤，生产初级一块组成的至少有一个SPAR公司生产每个附件的酒吧和酒吧在SPAR公司的形式，带不断加强和单向纤维是由烧结说，热塑性矩阵，得到的拉挤在熔化温度矩阵，数层的连续和单向纤维是由烧结说，矩阵，如果说，生根部分组成，至少有两个实习酒吧，每个人都分别延长一石酒吧，在叠加部分，相应的带形成的SPAR公司的一部分，居住在蚬壳公司，与干预的至少有一单层连续和单向纤维是由烧结说，矩阵之间的毗邻叠加条形零件，及装修一个可移动的工具，在形状，离间，部分之间举行的间隔从对方的两个邻国带，形成两个附件酒吧的生根部分，然后安排带在一个模具，并插入每个联系年底部分一拉挤带之间的二板的要素扣押，叠加所有层压板的要素扣押，关闭模具和压缩其内容的压力下和在熔化温度说，热塑性矩阵，并巩固矩阵冷却 rigidify该SPAR公司，从而获得与层压板的附着牢固重视其生根的一部分。

Others claimed that the Hessian soldier rose from the grave to lead the Hessian soldiers in a charge up nearby Chatterton Hill, not knowing that the hill had already been taken by the British.

另一些人则认为这个黑森士兵还不知道附近的查特顿山已被英国人占领，他从坟墓里出来便是要领导其他黑森士兵向那儿冲锋。

In order to avoid the Maratos effect,the merit function s used are approximations to Flether s differentiable exact penalty function,and the algorithm updates approximations to one-sided reduced Hessian and two-sided reduced Hessian seperately.

为避免Maratos效应，我们采用Flether的光滑精确罚函数的逼近形式作为价值函数，并且分别对Lagarange函数的单边既约Hessian的近似阵和双边既约Hessian的近似阵进行校正。

It is well-known that reduced Hessian method is one of the most efficient methods for solving large scale constrained optimization problems. However, the convergence analysis for the method requires of the positive definiteness of the reduced Hessian of Lagrangian function.

众所周知，既约Hessian方法是求解较大规模约束优化问题的一类有效方法，但已有的这类方法的全局收敛性分析需假定拉格朗日函数的既约Hessian矩阵的一致正定性。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

In Chapter 5, the least-squares solutions bisymmetric matrix set of the matrix equation ATXA = B on two linear manifolds Si ={X BSRnxn\\\XY - Z\\ = min} and S2 ={X BSRnXn\XY = Z, YtTZi = ZjYu ZtffYi = Zi,i = 1,2, Y, Z e Rnxm}, by applying the singular value decomposition of matrix and the canonical correlation decomposition of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = B on two linear manifolds.

在第五章，我们研究了两类线性流形S_1={X∈BSR~|‖XY-Z‖=min}和S_2={X∈BSR~|XY=Z，Y_i~TZ_i=Z_i~TY_i，Z_iY_i+Y_i=Z_i，i=1，2，Y，Z∈R~}上矩阵方程A~TXA=B的双对称最小二乘解。

From the history of Matrix and Transformation and the development of curriculum at home and abroad, putting matrix combined with the transformation, and orienting the study in 2×2 rank matrix, boosting matrix up the geometrical visualization as a algebra objects are a new perspective on knowing matrix.

从矩阵和变换的历史发展过程和国内外矩阵和变换的课程设置来看，把矩阵与变换相结合，并定位在2×2阶上研究矩阵，增强作为代数对象的矩阵的几何直观性，是认识矩阵的一个新视角。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑＞0时，众多文献讨论了回归系数阵的各种估计及LSE的有效性，本文考虑了当∑≥0的情形，给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计，研究了它的一个最大概率性质，并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件，在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计，定义了LSE相对于BLUE的一个相对效率，并给出了它的界。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。