A program based on MATLAB 7.0 platform was developed to locate characteristic peak position and calculate net area of characteristic peak.The formula for the calculation of relative standard deviation of net peak area...A program based on MATLAB 7.0 platform was developed to locate characteristic peak position and calculate net area of characteristic peak.The formula for the calculation of relative standard deviation of net peak area by Sterlinski’s method was found excellent in searching single peaks and resolving overlapping peaks in high resolution gamma-ray spectrum.Gaussian function fitting method using Levenberg-Marquardt algorithm was applied to calculate net area of peaks.A standard test spectrum supplied by the IAEA in 1995 was analyzed by the program and another two widely used commercial software.The analysis results show the program was superior to the latter two in searching single peaks and resolving overlapping peaks.The optimized fitting indexes are found between 0.962 and 0.996,which shows that the program adopted is feasible and accurate for extracting the net peak area in high resolution gamma-ray spectra.展开更多
Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad appl...Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.展开更多
基金Supported by National Natural Science Foundation of China(No.41174089 and 41164003)Open-ended Foundation(No.HJSJYB2010-07) from the Chinese Engineering Research Center
文摘A program based on MATLAB 7.0 platform was developed to locate characteristic peak position and calculate net area of characteristic peak.The formula for the calculation of relative standard deviation of net peak area by Sterlinski’s method was found excellent in searching single peaks and resolving overlapping peaks in high resolution gamma-ray spectrum.Gaussian function fitting method using Levenberg-Marquardt algorithm was applied to calculate net area of peaks.A standard test spectrum supplied by the IAEA in 1995 was analyzed by the program and another two widely used commercial software.The analysis results show the program was superior to the latter two in searching single peaks and resolving overlapping peaks.The optimized fitting indexes are found between 0.962 and 0.996,which shows that the program adopted is feasible and accurate for extracting the net peak area in high resolution gamma-ray spectra.
基金Chinese NSF grant 10231060the CAS Knowledge Innovation Program
文摘Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.
