A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the numbe...A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the number of evaluations of the polynomial)grows no faster than O(max{n^4,n^3log_2(n/ε)}).This work is in response to a question raised in a paper by S.Smale as to the efficiency of piecewise linear methods in solving equations.In comparison with a few results reported,the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.展开更多
The accurate identification of tea varieties is of great significance to ensure the interests of tea producers and consumers.As a non-destructive or micro damage detection method,laser-induced breakdown spectroscopy(L...The accurate identification of tea varieties is of great significance to ensure the interests of tea producers and consumers.As a non-destructive or micro damage detection method,laser-induced breakdown spectroscopy(LIBS)has been widely used in the quality detection or classification of agricultural products and food.The objective of this research was to automatically select optimal spectral peaks from the full LIBS spectra,and develop effective classification model for identifying tea varieties.The LIBS spectra covering the region 200-500 nm were measured for 600 Chinese tea leaves including six varieties(i.e.Longjing green tea,Jinhao black tea,Tie Guanyin,Huang Jinya,White peony tea,and Anhua dark tea).A total of 50 optimal spectral peaks were automatically selected from full LIBS spectra(6102)by using the uninformative variable elimination(UVE)and partial least squares projection analysis,and the selected spectral peaks mainly represent the elemental difference in C,Fe,Mg,Mn,Al and Ca.Partial Least Squares Discriminant Analysis(PLS-DA)was used for developing classification model using selected optimal spectral peaks,and yielded the 99.77%classification accuracy for 300 test samples was reached.The results indicate that the proposed method can be used to identify leaf varieties in various tea products.展开更多
基金This work is supported in part by the Foundation of Zhongshan University Advanced Research Centrein part by the National Natural Science Foundation of China
文摘A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the number of evaluations of the polynomial)grows no faster than O(max{n^4,n^3log_2(n/ε)}).This work is in response to a question raised in a paper by S.Smale as to the efficiency of piecewise linear methods in solving equations.In comparison with a few results reported,the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.
基金This work was financially supported by the National Natural Science Foundation of China(Grant no.61775086,61772240)the Fundamental Research Funds for the Central Universities(JUSRP51730A).
文摘The accurate identification of tea varieties is of great significance to ensure the interests of tea producers and consumers.As a non-destructive or micro damage detection method,laser-induced breakdown spectroscopy(LIBS)has been widely used in the quality detection or classification of agricultural products and food.The objective of this research was to automatically select optimal spectral peaks from the full LIBS spectra,and develop effective classification model for identifying tea varieties.The LIBS spectra covering the region 200-500 nm were measured for 600 Chinese tea leaves including six varieties(i.e.Longjing green tea,Jinhao black tea,Tie Guanyin,Huang Jinya,White peony tea,and Anhua dark tea).A total of 50 optimal spectral peaks were automatically selected from full LIBS spectra(6102)by using the uninformative variable elimination(UVE)and partial least squares projection analysis,and the selected spectral peaks mainly represent the elemental difference in C,Fe,Mg,Mn,Al and Ca.Partial Least Squares Discriminant Analysis(PLS-DA)was used for developing classification model using selected optimal spectral peaks,and yielded the 99.77%classification accuracy for 300 test samples was reached.The results indicate that the proposed method can be used to identify leaf varieties in various tea products.
