The traditional library least squares approach (LLS) is affected by the inconsistency of the statistical uncertainties of different channels in a gamma spectrum, which leads to large fluctuations in the analysis results. This work proposes a weighted library least squares approach (WLLS) that uses the square root of the count to weight the regression objective function and has implemented a verification experiment based on Prompt Gamma Neutron Activation Analysis (PGNAA). The results showed that, after weighing using the square root of the count, the fluctuation level of statistical uncertainty in the spectrum was reduced from 44.34 to 2.25. After the analysis of the WLLS approach, the average standard deviation of the results was reduced to at least 0.37 times that of the LLS approach.
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