使稀疏

The algorithm uses the wavelet decomposition and reconstruction in multi-resolution editing B-spline curves and transforms a zonal matrix or sparse matrix to a row simplified matrix using the properties of the augmented matrix of the system of linear equations,which is a zonal matrix or sparse matrix,by elementary row operation.

该算法利用方程组的增广矩阵为类带状矩阵或者稀疏矩阵这一特点，运用简单的矩阵的行初等变换，将类带状矩阵或者稀疏矩阵化成容易接受的行简化矩阵，解方程组，使小波分解与重构的过程快速准确，使从事相关工作的技术人员更容易理解和接受。

This paper presents a fast algorithm based on the measured equation of invariance.Conformal meshes are made along the surface of two-dimensional scatterer.Renumbering of nodes changed the original sparse matrix into band one,and the consumption of computer memory and CPU time decrease from O(N2) to O.Via this new algorithm,electrically large problem can now be rapidly solved.

提要 本文基于不变性测试方程法提出一种快速算法，在二维散射体表面建立共形差分网格后，通过对节点的重新排序，将原问题中的稀疏矩阵变换为带状稀疏阵，从而使占用的计算机内存和计算时间均由O(N2)下降为O，可以解决原来无法计算的问题。

To obtain a sparseness of support vector for least squares support vector regression, an algorithm called vector base learning is proposed in this paper.

使最小二乘支持向量机的解具有稀疏性，本文提出一种稀疏解算法——矢量基学习。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

The usual travel time tomography method is based on geometrical ray theory,however,it assumes that the seismic wave has very high frequency,which often makes the tomographic inversion have ill posed problem because of the sparse ray distribution in the model space and finally affects the reliability and resolution of the tomographic results.

基于几何射线理论的旅行时层析方法假设地震波频率足够高，这样往往由于射线存模型空间的稀疏分布，使层析反演问题具有严重的不适定性，从而极大地影响层析成像结果的可靠性和分辨率。

The principles are as follows:①preliminary interpretation is carried out on crosswell seismic data in depth domain to establish an accurate velocity model;②sinc interpolating function is used in depth-time conversion to realize waveform fidelity;③the recognition of surface seismic data is utilized to ascertain the reflection characteristics of crosswell seismic data in time domain;④ good spatial continuity of surface seismic data is adopted to retrieve the "hopper" defect in crosswell seismic profiles and the deficiency of lateral contrast between crosswell seismic data;⑤in fine calibration of well-side traces of crosswells and surface seismic data, coincident time-depth relation is used to match two seismic data so as to make the calibration more reasonable;⑥in multi-crosswell seismic data inversion by sparse spike inversion method, lateral restraints are strengthened to ensure the continuity of inversed wave impedance profile.

实现反演的基本原理是：对深度域井间地震资料进行初步解释；建立精确的速度模型；在对井间地震剖面进行深时转换时采用sinc插值函数实现波形保真；利用对地面地震资料的认识来落实时间域井间地震资料的反射特征；利用地面地震资料良好的空间连续性弥补井间地震剖面的"漏斗"缺陷和井间资料之间横向对比性的不足；在井间地震和地面地震井旁道精细标定中，通过一致的时深关系来实现两种地震资料之间的匹配，使井旁道的标定更加合理；在利用稀疏脉冲反演方法进行连井井间地震资料反演时，通过增强横向约束保证反演波阻抗剖面的连续性。

Based on ear recognition, an improved NMFSC(Nonnegative Matrix Factorization with Sparseness Constraints) method was proposed by imposing an additional constraint on the objective function of NMFSC, which could capture the semantic relations of coefficient matrix as orthogonal as possible. The interated rules to solve the objective function with the constraint were presented, and its convergence was proved.

针对人耳识别问题，提出了一种改进的稀疏性受限的非负矩阵因子方法，通过增加一个使系数矩阵尽可能正交的约束条件来定义原目标函数，给出求解该目标函数的迭代规则，并证明迭代规则的收敛性。

Based on ear recognition, an improved NMFSC (Non-negative Matrix Factorization with Sparseness Constraints) method was proposed by imposing an additional constraint on the objective function of NMFSC, which could capture the semantic relations of coefficient matrix as orthogonal as possible. The interated rules to solve the objective function with the constraint were presented, and its convergence was proved.

针对人耳识别问题，提出了一种改进的稀疏性受限的非负矩阵因子方法，通过增加一个使系数矩阵尽可能正交的约束条件来定义原目标函数，给出求解该目标函数的迭代规则，并证明迭代规则的收敛性。

In order to seamlessly combine NSGA-Ⅱ and the greatly different MOPSO, the special concepts (particle and its velocity, Pbest and leader) for MOPSO were dealt with within the scope of NSGA-Ⅱ: 1 particle in MOPSO was considered to be equivalent to offspring individual in NSGA-Ⅱ; 2 the concept of velocity fell into disuse; 3 the concept of Pbest also came into disuse. Instead of that, for each dimension of a particle, the nearest one among its nondominated individuals in parent population was used; 4 the leader of a particle was the individual with largest sparse degree among parent population or selected from parent population by binary tournament selection method, which of them taking effect lies on the predefined probability. In addition, a new concept, i.

为使这两种差异较大的算法实现无缝融合，在NSGA-Ⅱ算法范围内对MOPSO中特有的概念粒子及其速度、Pbest、引导者进行处理：1粒子对应于NSCA-Ⅱ中子代群体的个体；2不再使用粒子速度概念；3不再使用粒子Pbest概念，代之以从父代群体中为每个粒子的每一维寻找一个最近的该粒子非支配个体；4每一个粒子的引导者可以是父代群体中稀疏程度最大的个体或者是按照二进制随机竞赛选择方法从父代群体中选择的一个个体，具体哪一种方式发挥作用依赖于预先设定的概率。

For large sparse matrix,it is very important to keep the sparse of matrix in computation.

引言 在实际计算中，我们常常碰到一类大稀疏矩阵，这类矩阵由于它本身的稀疏性，我们除了研究它的计算量外，更重要的是使这类稀疏矩阵在计算中仍然保持其稀疏性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。