This paper presents a modified hybrid three-term conjugate gradient projection method(MHTTCGPM)for solving large-scale nonlinear monotone equations with convex set constraints.The method incorporates an adaptive line ...This paper presents a modified hybrid three-term conjugate gradient projection method(MHTTCGPM)for solving large-scale nonlinear monotone equations with convex set constraints.The method incorporates an adaptive line search technique,ensuring that the search direction satisfies the sufficient descent property.Without requiring Lipschitz continuity,the global convergence of the proposed method is rigorously established.Numerical results demonstrate the effectiveness and reliability of the new algorithm.展开更多
The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an ...The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.展开更多
The computational problem of fourth power mean of generalized three-term exponential sums is studied by using the trigonometric identity and the properties of the reduced residue system. Some explicit formulas for the...The computational problem of fourth power mean of generalized three-term exponential sums is studied by using the trigonometric identity and the properties of the reduced residue system. Some explicit formulas for the fourth power mean of generalized three-term exponential sums under different conditions are given.展开更多
In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with...In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.展开更多
In this paper, a new Wolfe-type line search and a new Armijo-type line searchare proposed, and some global convergence properties of a three-term conjugate gradient method withthe two line searches are proved.
In this paper,an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration.Different from the existent methods,a dynam...In this paper,an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration.Different from the existent methods,a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed.Under mild condition,we show that the proposed method converges globally.Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.展开更多
鉴于酒店行业在线评价体系的复杂性及其对目标市场定位的重要性,本文通过分析在线评论、优化酒店服务与潜在顾客之间的匹配度,创新性地提出了一种新的酒店推荐算法,旨在提高复杂情景下推荐结果的准确性,提升顾客满意度及酒店的市场竞争...鉴于酒店行业在线评价体系的复杂性及其对目标市场定位的重要性,本文通过分析在线评论、优化酒店服务与潜在顾客之间的匹配度,创新性地提出了一种新的酒店推荐算法,旨在提高复杂情景下推荐结果的准确性,提升顾客满意度及酒店的市场竞争力。首先,描述研究问题,突出筛选机制在电子商务交易匹配系统中的重要性。其次,为尽可能地保留原始评论数据,引入复杂信息表征工具,将文本形式的在线评论转化为概率语言术语集(probabilistic linguistic term sets,PLTSs)信息。再次,考虑海量的评论主体通常具有不同犹豫程度的偏好,考虑悲观和乐观偏好,提出一种基于不完全模糊关系的双极偏好权重分配方法。接着,结合高斯混合聚类算法,提出概率语言环境下的分布熵惩罚-高斯混合(DEPGMM)聚类算法,并获取在线评论隶属于不同类别的条件概率,进而获得聚类等价类。进一步,引入三支决策理论方法,给出面向智能推荐的概率语言三支决策过程。最后,通过对三家酒店筛选排序,结合参数分析和对比分析验证所提出方法的有效性和可行性。展开更多
基金supported by the National Natural Science Foundation of China(No.12271518)the Key Program of the National Natural Science Foundation of China(No.62333016)。
文摘This paper presents a modified hybrid three-term conjugate gradient projection method(MHTTCGPM)for solving large-scale nonlinear monotone equations with convex set constraints.The method incorporates an adaptive line search technique,ensuring that the search direction satisfies the sufficient descent property.Without requiring Lipschitz continuity,the global convergence of the proposed method is rigorously established.Numerical results demonstrate the effectiveness and reliability of the new algorithm.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1137129161202437)
文摘The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.
基金Supported by the National Natural Science Foundation of China(Grant No.11571277)the Science and Technology Program of Shaanxi Province(Grant Nos.2014JM1007+2 种基金2014KJXX-612016GY-0802016GY-077)
文摘The computational problem of fourth power mean of generalized three-term exponential sums is studied by using the trigonometric identity and the properties of the reduced residue system. Some explicit formulas for the fourth power mean of generalized three-term exponential sums under different conditions are given.
文摘In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.
基金This research is supported by the National Natural Science Foundation of China(10171055).
文摘In this paper, a new Wolfe-type line search and a new Armijo-type line searchare proposed, and some global convergence properties of a three-term conjugate gradient method withthe two line searches are proved.
基金This work was supported by First-Class Disciplines Foundation of Ningxia Hui Autonomous Region(No.NXYLXK2017B09)the National Natural Science Foundation of China(Nos.11601012,11861002,71771030)+3 种基金the Key Project of North Minzu University(No.ZDZX201804)Natural Science Foundation of Ningxia Hui Autonomous Region(Nos.NZ17103,2018AAC03253)Natural Science Foundation of Guangxi Zhuang Autonomous Region(No.2018GXNSFAA138169)Guangxi Key Laboratory of Cryptography and Information Security(No.GCIS201708).
文摘In this paper,an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration.Different from the existent methods,a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed.Under mild condition,we show that the proposed method converges globally.Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.
文摘鉴于酒店行业在线评价体系的复杂性及其对目标市场定位的重要性,本文通过分析在线评论、优化酒店服务与潜在顾客之间的匹配度,创新性地提出了一种新的酒店推荐算法,旨在提高复杂情景下推荐结果的准确性,提升顾客满意度及酒店的市场竞争力。首先,描述研究问题,突出筛选机制在电子商务交易匹配系统中的重要性。其次,为尽可能地保留原始评论数据,引入复杂信息表征工具,将文本形式的在线评论转化为概率语言术语集(probabilistic linguistic term sets,PLTSs)信息。再次,考虑海量的评论主体通常具有不同犹豫程度的偏好,考虑悲观和乐观偏好,提出一种基于不完全模糊关系的双极偏好权重分配方法。接着,结合高斯混合聚类算法,提出概率语言环境下的分布熵惩罚-高斯混合(DEPGMM)聚类算法,并获取在线评论隶属于不同类别的条件概率,进而获得聚类等价类。进一步,引入三支决策理论方法,给出面向智能推荐的概率语言三支决策过程。最后,通过对三家酒店筛选排序,结合参数分析和对比分析验证所提出方法的有效性和可行性。
