查询词典 Jacobi method

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

In the second part, we gave several basic and essential knowledge of inverse eigenvalue problems for Jacobi matrices: such as the properties of tridiagonal matrices, Jacobi matrices, orthogonal polynomials, Gauss quadrature formula and inverse eigenvalue problem for Jacobi matrices.

第二部分介绍了求解Jacobi矩阵反问题的基础：三对角矩阵和Jacobi矩阵，正交多项式，高斯积分方法的性质和Jacobi矩阵特征值反问题。

When the coefficient matrice is index p cycle matrice (p = 3,4,5),we educe the relation between preconditionging Jacobi 、 GS iterative matrices" and classical Jacobi iterative matrices" eigenvalue; As an application, make some preconditioning iterative factors, when classical Jacobi iterative converge, the preconditioning iterative methods may converge faster.

2系数矩阵是指数p=3，4，5循环矩阵时，分别给出了预条件Jacobi、Gauss-Seidel迭代矩阵与传统块Jacobi迭代矩阵二者特征值之间的关系，作为一个应用，通过预条件因子的特殊取值，使传统Jacobi迭代收敛时，预条件块迭代法的收敛速度成倍提高。

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

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

In chapter 3,we study the Zakharov-Kuznetsov-Modified Equal-Width equation by employing the extended Jacobi elliptic function expansion method and obtain some new solutions of Jacobi elliptic function type of the ZK-MEW equation.;Secondly,using sn-cn method,we study K(m,n,1) equation and obtained some new exact solutions when k=s=3,especially obtained abundand solitary solutions and trigonometric function solutions when m→0 and m→1;In chapter 4,Painleve singular analysis was applied to nonlinear PDE with variable coefficients.

第四章将Painleve奇性分析方法应用到带阻尼项的变系数Burgers方程中，并得到了该类Burgers方程具有Painleve性质的条件，给出了该类Burgers方程的Backlund变换，用所得Backlund变换得到了若干精确孤立波解，包括奇异孤立波解，这些解不等同于行波型孤立波解；用齐次平衡法得到了对数型DBM方程的Backlund变换，并获得了DBM方程的各种孤立波解，包括尖峰孤立波解和奇异尖峰孤立波解。

Second, Jacobi elliptic function expanded methods proposed by Liu et al and its evolution and extendedness currently including double Jacobi elliptic function expanded method and F expanded method of solving nonlinear equations were introduced.

二、介绍刘等人提出的Jacobi椭圆函数展开法及当前一些主要的扩展——双Jacobi椭圆函数展开法和F展开法。

Fourth, at basic of the improvement of Jacobi elliptic function expanded method, the extended Jacobi elliptic function expanded methods was proposed.

四、对Jacobi椭圆函数展开法进行改进和扩展，提出新的扩展的Jacobi椭圆展开法来求解非线性发展方程并得到许多新的周期波解。

Based on a relationship between the RF and Jacobi matrix, a novel method which is independent of the forward modeling for a fast algorithm of Jacobi matrix employing the RF was advanced.

通过建立二维非均质反演Jacobi矩阵与响应函数的关系，开辟了Jacobi矩阵快速算法构造的有效途径。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。