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Nearest lattice point algorithms on semi k-reduced basis

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Science in China(Series F) 2003年第6期46卷 485-494页

作者：阚海斌沈鸿 Department of Computer Science and Engineering Fudan UniversityShanghai 200433China Graduate School and Information ScienceJapan Advanced Institute of Science and Technology1-1AsahidaiTatsunokuchiIshikawa 923-1292Japan Graduate School and Information Science Japan Advanced Institute of Science and Technology1-1AsahidaiTatsunokuchiIshikawa923-1292Japan

In this paper, we firstly generalize the relations among the basis vectors of LLL reduced basis to semi k-reduced basis. Then we analyze the complexities of the nearest plane algorithm and round-off algorithm on semi k-reduced basis, which, compared with L. Babai's results on LLL reduced basis, have better approximate ratios and contain almost the same time complexities.

关键词： lattice reduced basis nearest plane algorithm.

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

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Communications in Mathematical Research 2020年第2期36卷 154-192页

作者： Junlong Lyu Zhiwen Zhang Department of Mathematics The University of Hong KongPokfulam RoadHong Kong SARChina

We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query *** method consists of offline and online *** the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis *** the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale *** MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the *** have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random ***,we provide convergence analysis of the proposed *** results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.

关键词： Random partial differential equations(RPDEs) uncertainty quantification(UQ) multiscale finite element method(MsFEM) multilevel Monte Carlo(MLMC) reduced basis convergence analysis

F[x]-lattice basis reduction algorithm and multisequence synthesis

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Science in China(Series F) 2001年第5期44卷 321-328页

作者：王丽萍祝跃飞 DepartmentofAppliedMathematics InformationEngineeringUniversityZhengzhou450002China StateKeyLaboratoryofInformationSecurity Beijing100039China

By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field F. Its computational complexity is O(N2) operations in F where N is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomi-als is given. The set and exact number of all minimal polynomials are also described when F is a finite field.

关键词： multisequence shift-register synthesis F[x]-lattice basis reduction algorithm reduced basis normal reduced basis.