大规模多输入多输出(Multiple-Input Multiple-Output,MIMO)系统由于具备较多的天线数,会导致传统线性信号检测算法如最小均方误差(Minimum Mean Square Error,MMSE)的复杂度过高。针对以上问题,提出了F修正的自适应超松弛迭代(F-correc...大规模多输入多输出(Multiple-Input Multiple-Output,MIMO)系统由于具备较多的天线数,会导致传统线性信号检测算法如最小均方误差(Minimum Mean Square Error,MMSE)的复杂度过高。针对以上问题,提出了F修正的自适应超松弛迭代(F-corrected Adaptive Successive over Relaxation,FA-SOR)检测算法。该算法首先利用超松弛迭代(Successive over Relaxation,SOR)算法避免高阶矩阵求逆运算,降低复杂度;其次使用F修正的公式自动更新SOR算法迭代使用的松弛参数,同时优化迭代的公式与初始解来加快收敛速度。仿真结果表明,不论在理想独立信道还是相关信道下,相比于现有的自适应SOR算法,FA-SOR都能以更低的复杂度达到更低的误码率,同时逼近MMSE算法的性能。展开更多
In order to solve the linear algebraic system AX=b in complex domain, where A is a weakly cyclic of index p=3 matrix (p cyclic matrix), the convergence properties of SOR are studied in the paper. In section 1, we give...In order to solve the linear algebraic system AX=b in complex domain, where A is a weakly cyclic of index p=3 matrix (p cyclic matrix), the convergence properties of SOR are studied in the paper. In section 1, we give some definitions. In section 2, the necessary conditions for convergent complex SOR are given moreover the necessary and sufficient conditions in some special situations are also presented. In section 3, we expand the techniques applied by R.S. Varga et al., and it is established that the results of R.S. Varga et. al. are special cases of our work.展开更多
本文介绍了基于统一计算设备架构(Compute Unified Device Architecture,CUDA)的图形处理器(Graphic Processing Unit,GPU)计算环境在钍基熔盐堆(Thorium Molten Salt Reactor,TMSR)设计平台的建立,并将反应堆球场计算软件SRAC(Structur...本文介绍了基于统一计算设备架构(Compute Unified Device Architecture,CUDA)的图形处理器(Graphic Processing Unit,GPU)计算环境在钍基熔盐堆(Thorium Molten Salt Reactor,TMSR)设计平台的建立,并将反应堆球场计算软件SRAC(Structure Research and Analysic Corporation)的中子三维扩散计算模块移植到GPU上进行测试及结果验证。采用中心点差分方法推导出三维扩散计算的差分方程,并用超松弛迭代法(Successive Over Relaxation Method,SOR)求解φ,研究了SOR迭代算法的并行实现过程。结果表明,移植的GPU模块部分计算正确,计算速度得到有效提升,验证了TMSR设计平台在GPU计算环境下可正常工作。展开更多
Three types of previously used numerical methods are revisited for computing the streamfunctionψand velocity potentialχfrom the horizontal velocity v in limited domains.The first type,called the SOR-based method,use...Three types of previously used numerical methods are revisited for computing the streamfunctionψand velocity potentialχfrom the horizontal velocity v in limited domains.The first type,called the SOR-based method,uses a classical successive over-relaxation(SOR)scheme to computeψ(orχ)first with an arbitrary boundary condition(BC)and thenχ(orψ)with the BC derived from v.The second type,called the spectral method,uses spectral formulations to construct the inner part of(ψ,χ)-the inversion of(vorticity,divergence)with a homogeneous BC,and then the remaining harmonic part of(ψ,χ)with BCs from v.The third type,called the integral method,uses integral formulas to compute the internally induced(ψ,χ)-the inversion of domain-internal(vorticity,divergence)using the free-space Greenꞌs function without BCs and then the remaining harmonicψ(orχ)with BCs from v minus the internally-induced part.Although these methods have previously been successfully applied to flows in large-scale and synoptic-scale domains,their accuracy is compromised when applied to complex flows over mesoscale domains,as shown in this paper.To resolve this problem,two hybrid approaches,the integral-SOR method and the integral-spectral method,are developed by combining the first step of the integral method with the second step adopted from the SOR-based and spectral methods,respectively.Upon testing these methods on real-case complex flows,the integral-SOR method is significantly more accurate than the integral-spectral method,noting that the latter is still generally more accurate than the three previously-used methods.The integral-SOR method is recommended for future applications and diagnostic studies of complex flows.展开更多
The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional ...The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.展开更多
借鉴分类问题的算法,推广到回归问题中去,针对用于分类问题的SOR(successive overrelaxation for support vector)支持向量机算法,提出SORR(successive overrelaxation for support vector regression)支持向量回归算法,并应用于医学上...借鉴分类问题的算法,推广到回归问题中去,针对用于分类问题的SOR(successive overrelaxation for support vector)支持向量机算法,提出SORR(successive overrelaxation for support vector regression)支持向量回归算法,并应用于医学上三类血浆脂蛋白(VLDL、LDL、HDL)测定样本中胆固醇的含量。数值实验表明:SORR算法有效,与标准的支持向量回归SVR算法相比,保持了相同的回归精度,提高了学习速度,为临床上测定胆固醇含量提供新的有效方法。展开更多
文摘大规模多输入多输出(Multiple-Input Multiple-Output,MIMO)系统由于具备较多的天线数,会导致传统线性信号检测算法如最小均方误差(Minimum Mean Square Error,MMSE)的复杂度过高。针对以上问题,提出了F修正的自适应超松弛迭代(F-corrected Adaptive Successive over Relaxation,FA-SOR)检测算法。该算法首先利用超松弛迭代(Successive over Relaxation,SOR)算法避免高阶矩阵求逆运算,降低复杂度;其次使用F修正的公式自动更新SOR算法迭代使用的松弛参数,同时优化迭代的公式与初始解来加快收敛速度。仿真结果表明,不论在理想独立信道还是相关信道下,相比于现有的自适应SOR算法,FA-SOR都能以更低的复杂度达到更低的误码率,同时逼近MMSE算法的性能。
文摘In order to solve the linear algebraic system AX=b in complex domain, where A is a weakly cyclic of index p=3 matrix (p cyclic matrix), the convergence properties of SOR are studied in the paper. In section 1, we give some definitions. In section 2, the necessary conditions for convergent complex SOR are given moreover the necessary and sufficient conditions in some special situations are also presented. In section 3, we expand the techniques applied by R.S. Varga et al., and it is established that the results of R.S. Varga et. al. are special cases of our work.
文摘本文介绍了基于统一计算设备架构(Compute Unified Device Architecture,CUDA)的图形处理器(Graphic Processing Unit,GPU)计算环境在钍基熔盐堆(Thorium Molten Salt Reactor,TMSR)设计平台的建立,并将反应堆球场计算软件SRAC(Structure Research and Analysic Corporation)的中子三维扩散计算模块移植到GPU上进行测试及结果验证。采用中心点差分方法推导出三维扩散计算的差分方程,并用超松弛迭代法(Successive Over Relaxation Method,SOR)求解φ,研究了SOR迭代算法的并行实现过程。结果表明,移植的GPU模块部分计算正确,计算速度得到有效提升,验证了TMSR设计平台在GPU计算环境下可正常工作。
基金supported by the National Natural Science Foundation of China under Grant Nos. 91937301, 41875074, and 41675060the Second Tibetan Plateau Comprehensive Scientific Expedition 2019QZKK0104+1 种基金the National Key Scientific and Technological Infrastructure Project “EarthLab”provided by NOAA/OAR under NOAA–OU Cooperative Agreement #NA16OAR4320072, U.S. Department of Commerce
文摘Three types of previously used numerical methods are revisited for computing the streamfunctionψand velocity potentialχfrom the horizontal velocity v in limited domains.The first type,called the SOR-based method,uses a classical successive over-relaxation(SOR)scheme to computeψ(orχ)first with an arbitrary boundary condition(BC)and thenχ(orψ)with the BC derived from v.The second type,called the spectral method,uses spectral formulations to construct the inner part of(ψ,χ)-the inversion of(vorticity,divergence)with a homogeneous BC,and then the remaining harmonic part of(ψ,χ)with BCs from v.The third type,called the integral method,uses integral formulas to compute the internally induced(ψ,χ)-the inversion of domain-internal(vorticity,divergence)using the free-space Greenꞌs function without BCs and then the remaining harmonicψ(orχ)with BCs from v minus the internally-induced part.Although these methods have previously been successfully applied to flows in large-scale and synoptic-scale domains,their accuracy is compromised when applied to complex flows over mesoscale domains,as shown in this paper.To resolve this problem,two hybrid approaches,the integral-SOR method and the integral-spectral method,are developed by combining the first step of the integral method with the second step adopted from the SOR-based and spectral methods,respectively.Upon testing these methods on real-case complex flows,the integral-SOR method is significantly more accurate than the integral-spectral method,noting that the latter is still generally more accurate than the three previously-used methods.The integral-SOR method is recommended for future applications and diagnostic studies of complex flows.
基金supported by the National Natural Science Foundation of China(No.10771031)the Fundamental Research Funds for Central Universities(No.090405013)
文摘The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.
文摘借鉴分类问题的算法,推广到回归问题中去,针对用于分类问题的SOR(successive overrelaxation for support vector)支持向量机算法,提出SORR(successive overrelaxation for support vector regression)支持向量回归算法,并应用于医学上三类血浆脂蛋白(VLDL、LDL、HDL)测定样本中胆固醇的含量。数值实验表明:SORR算法有效,与标准的支持向量回归SVR算法相比,保持了相同的回归精度,提高了学习速度,为临床上测定胆固醇含量提供新的有效方法。
