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求递归数列通项的线性代数解法
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作者 于友文 黎树人 《河池师范高等专科学校学报》 2000年第4期19-22,共4页
本文介绍求线性递归数列。
关键词 通项 线性代数解法 线性递归数列 分式线性递归数列 递推关系
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物理计算的保真与代数动力学算法——V.非线性对流方程的代数动力学解法与算法 被引量:4
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作者 张华 卢伟涛 王顺金 《中国科学(G辑)》 CSCD 2008年第8期1028-1037,共10页
把非线性偏微分方程的代数动力学解法和算法用于非线性对流方程,检验了这一方法对非线性对流方程的解析求解和数值求解的有效性.
关键词 对流方程 泛函空间的代数动力学 线性对流方程的代数动力学解法与算法
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A Study for Obtaining New and More General Solutions of Special-Type Nonlinear Equation 被引量:1
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作者 ZHAO Hong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第6期1013-1016,共4页
The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions... The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions. 展开更多
关键词 special-type nonlinear equations generalized algebraic method travelling wave solutions
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A Class of Third-order Convergence Variants of Newton's Method
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作者 ZHAO Ling-ling WANG Xia 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第2期165-170,共6页
A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton's method, are given. Their convergence properties are proved. They are at least third order convergence nea... A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton's method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton's methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application. 展开更多
关键词 variant Newton's methods third-order convergence numerical test
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Analytical Results of Eigenstates and Eigenenergies for Three Kinds of Models Describing N-mode Multiphoton Process
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作者 YANGWen-Xing LIJia-Hua +2 位作者 LIWei-Bin CHENAi-Xi JINLi-Xia 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第1期22-26,共5页
We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical res... We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure. 展开更多
关键词 SPECTRUM EIGENSTATE EIGENVALUE
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Variational algorithms for linear algebra 被引量:1
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作者 Xiaosi Xu Jinzhao Sun +3 位作者 Suguru Endo Ying Li Simon C.Benjamin Xiao Yuan 《Science Bulletin》 SCIE EI CSCD 2021年第21期2181-2188,M0003,共9页
Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational... Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%. 展开更多
关键词 Quantum computing Quantum simulation Linear algebra Matrix multiplication Variational quantum eigensolver
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An efficient algorithm for factoring polynomials over algebraic extension field 被引量:1
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作者 SUN Yao WANG DingKang 《Science China Mathematics》 SCIE 2013年第6期1155-1168,共14页
An efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its CrSbner basis, no extra Grbbner ... An efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its CrSbner basis, no extra Grbbner basis computation is needed for factoring a polynomial over this extension field. Nothing more than linear algebraic technique is used to get a characteristic polynomial of a generic linear map. Then this polynomial is factorized over the ground field. From its factors, the factorization of the polynomial over the extension field is obtained. The algorithm has been implemented in Magma and computer experiments indicate that it is very efficient, particularly for complicated examples. 展开更多
关键词 algorithm FACTORIZATION algebraic extension field
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Sparse bivariate polynomial factorization
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作者 WU WenYuan CHEN JingWei FENG Yong 《Science China Mathematics》 SCIE 2014年第10期2123-2142,共20页
Motivated by Sasaki's work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynom... Motivated by Sasaki's work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is etIicient, especially for sparse bivariate polynomials. 展开更多
关键词 polynomial factorization sparse polynomial generalized Hensel lifting
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