A new method for the resolution and quantitative kinetic analysis of overlapping electron paramagnetic (EPR) spectra, based on a combination of smoothing by B-splines and/or discrete cosine transformation and linear algebra methods for finding eigenvalues and eigenvectors of the covariance matrix using the Frobenius normal form with subsequent final basis adjustment by the Moore–Penrose pseudo-inverse matrix, is proposed. This algorithm does not require the use of the time-consuming multiple iterations of the least squares method. Our approach has been tested on several specific chemical systems including stable organic radicals and paramagnetic V⁴⁺ and VO²⁺ ions. In all the cases, the analysis of experimental EPR spectra demonstrated that the new approach produces good results.

一种用于重叠电子顺磁 (EPR) 谱的分辨率和定量动力学分析的新方法，基于B样条和/或离散余弦变换的平滑和线性代数方法的组合，用于查找协方差矩阵的特征值和特征向量使用提出了 Frobenius 范式，随后通过 Moore-Penrose 伪逆矩阵进行最终基调整。该算法不需要使用最小二乘法耗时的多次迭代。我们的方法已经在几个特定的​​化学系统上进行了测试，包括稳定的有机自由基和顺磁性 V ⁴⁺和 VO ²⁺离子。在所有情况下，对实验 EPR 光谱的分析表明，新方法产生了良好的结果。