Nonlinear-least-squares analysis of slow-motion EPR spectra in one and two dimensions using a modified Levenberg-Marquardt algorithm
Nonlinear-least-squares analysis of slow-motion EPR spectra in one and two dimensions using a modified Levenberg-Marquardt algorithm
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DOI：
10.1006/jmra.1996.0113
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发表时间：
1996-06-01
期刊：
影响因子：
--
通讯作者：
Freed, JH
中科院分区：
文献类型：
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作者：
Budil, DE;Lee, S;Freed, JH
应用Levenberg-Marquardt最小化算法的“模型信赖域”修正来分析一维CW EPR和多维傅里叶变换（FT）EPR谱，特别是在慢运动状态下。描述慢运动的动力学参数由基于随机Liouville方程（SLE）的模型计算与实验光谱的最小二乘拟合获得。信赖域方法固有地比标准Levenberg-Marquardt算法更有效，并且该过程的效率可以通过分离变量方法，其中拟合参数的子集在每次迭代中独立地最小化，从而减少了通过非线性最小二乘法拟合的参数的数量。该方法的一个特别有用的应用发生在多组分光谱的拟合中，对于该多组分光谱，可以通过分离变量法获得每个组分的相对总体。这些优点，结合最近改进的计算方法，用于解决SLE，导致了一个数量级的减少计算时间，并有可能进行交互式，实时拟合的实验室工作站与图形界面，拟合的实验数据的例子，包括多组分CW EPR谱以及二维和三维FT EPR谱，重点放在分析信息，可从算法中使用的偏导数，以及它如何可能被用来估计的条件和唯一性的拟合，以及估计置信限的参数在某些情况下。(C)出版社：Academic Press，Inc.
The application of the ''model trust region'' modification of the Levenberg-Marquardt minimization algorithm to the analysis of one-dimensional CW EPR and multidimensional Fourier-transform (FT) EPR spectra especially in the slow-motion regime is described. The dynamic parameters describing the slow motion are obtained from least-squares fitting of model calculations based on the stochastic Liouville equation (SLE) to experimental spectra, The trust-region approach is inherently more efficient than the standard Levenberg-Marquardt algorithm, and the efficiency of the procedure may be further increased by a separation-of-variables method in which a subset of fitting parameters is independently minimized at each iteration, thus reducing the number of parameters to be fitted by nonlinear least squares. A particularly useful application of this method occurs in the fitting of multicomponent spectra, for which it is possible to obtain the relative population of each component by the separation-of-variables method. These advantages, combined with recent improvements in the computational methods used to solve the SLE, have led to an order-of-magnitude reduction in computing time, and have made it possible to carry out interactive, real-time fitting on a laboratory workstation with a graphical interface, Examples of fits to experimental data will be given, including multicomponent CW EPR spectra as well as two- and three-dimensional FT EPR spectra, Emphasis is placed on the analytic information available from the partial derivatives utilized in the algorithm, and how it may be used to estimate the condition and uniqueness of the fit, as well as to estimate confidence limits for the parameters in certain cases. (C) 1996 Academic Press, Inc.