This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
约束二维有限脉冲响应(Finite Impulse Response,FIR)滤波器,现有设计算法计算复杂度高.针对二维FIR滤波器的约束最小二乘设计,本文应用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM),研究其并行优化方法.通过模...约束二维有限脉冲响应(Finite Impulse Response,FIR)滤波器,现有设计算法计算复杂度高.针对二维FIR滤波器的约束最小二乘设计,本文应用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM),研究其并行优化方法.通过模型的最大分划,并采用一种松弛技术,提出一个具有高度并行结构的最大分划松弛ADMM算法,分析了算法的计算复杂度,讨论了算法的收敛性,并给出了算法的参数设置方法.实验表明,最大分划松弛ADMM比非松弛的最大分划ADMM收敛快很多;与现有算法相比,提高了计算效率.GPU加速实验中获得的大加速比,表明了所提算法的高度并行性和可扩展性,在图像处理、计算机视觉、模式识别及机器学习等领域有广阔的应用前景.展开更多
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
文摘约束二维有限脉冲响应(Finite Impulse Response,FIR)滤波器,现有设计算法计算复杂度高.针对二维FIR滤波器的约束最小二乘设计,本文应用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM),研究其并行优化方法.通过模型的最大分划,并采用一种松弛技术,提出一个具有高度并行结构的最大分划松弛ADMM算法,分析了算法的计算复杂度,讨论了算法的收敛性,并给出了算法的参数设置方法.实验表明,最大分划松弛ADMM比非松弛的最大分划ADMM收敛快很多;与现有算法相比,提高了计算效率.GPU加速实验中获得的大加速比,表明了所提算法的高度并行性和可扩展性,在图像处理、计算机视觉、模式识别及机器学习等领域有广阔的应用前景.
