人工智能(AI)和物联网(IoT)技术的迅速发展,对计算能效提出了更高的要求,终端设备在硬件资源开销方面同样面临巨大挑战.为了应对能效问题,新型低功耗近似计算单元的设计得到了广泛研究.在数字信号处理和图像处理等应用场景中,存在大量...人工智能(AI)和物联网(IoT)技术的迅速发展,对计算能效提出了更高的要求,终端设备在硬件资源开销方面同样面临巨大挑战.为了应对能效问题,新型低功耗近似计算单元的设计得到了广泛研究.在数字信号处理和图像处理等应用场景中,存在大量的浮点运算.这些应用消耗了大量的硬件资源,但它们具有一定的容错性,没有必要进行完全精确的计算.据此,提出了一种基于移位近似算法MTA(multiplication to shift addition)和非对称截断的单精度可重构近似浮点乘法器设计方法.首先,采用了一种低功耗的近似算法MTA,将部分操作数的乘法运算转换为移位加法.其次,为了在精度和成本之间取得平衡,设计了针对操作数高有效位的非对称截断处理,并对截断后保留的部分进行精确计算.通过采用不同位宽的MTA近似计算和改变截断后部分积阵列的行数,生成了广阔的设计空间,从而可以在精度和成本之间进行多种权衡调整.与精确浮点乘法器相比,所提出设计MTA5T5的精度损失(MRED)仅约为0.32%,功耗降低了85.80%,面积减少了79.53%.对于精度较低的MTA3T3,其精度损失约为1.92%,而功耗和面积分别降低了90.55%和85.80%.最后,进行了FIR滤波和图像处理的应用测试,结果表明所提出的设计在精度和开销方面具有显著优势.展开更多
We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results ...We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.展开更多
In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
文摘人工智能(AI)和物联网(IoT)技术的迅速发展,对计算能效提出了更高的要求,终端设备在硬件资源开销方面同样面临巨大挑战.为了应对能效问题,新型低功耗近似计算单元的设计得到了广泛研究.在数字信号处理和图像处理等应用场景中,存在大量的浮点运算.这些应用消耗了大量的硬件资源,但它们具有一定的容错性,没有必要进行完全精确的计算.据此,提出了一种基于移位近似算法MTA(multiplication to shift addition)和非对称截断的单精度可重构近似浮点乘法器设计方法.首先,采用了一种低功耗的近似算法MTA,将部分操作数的乘法运算转换为移位加法.其次,为了在精度和成本之间取得平衡,设计了针对操作数高有效位的非对称截断处理,并对截断后保留的部分进行精确计算.通过采用不同位宽的MTA近似计算和改变截断后部分积阵列的行数,生成了广阔的设计空间,从而可以在精度和成本之间进行多种权衡调整.与精确浮点乘法器相比,所提出设计MTA5T5的精度损失(MRED)仅约为0.32%,功耗降低了85.80%,面积减少了79.53%.对于精度较低的MTA3T3,其精度损失约为1.92%,而功耗和面积分别降低了90.55%和85.80%.最后,进行了FIR滤波和图像处理的应用测试,结果表明所提出的设计在精度和开销方面具有显著优势.
基金supported by the Fundamental Research Funds for the Central Universities(2024KYJD2006).
文摘We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
