Fast matrix decomposition for DOSY using the eigenvalue decomposition and the difference approximation

Abstract

This paper deals with DOSY analysis method for a molecular structure analysis. DOSY analysis method is formulated as a matrix decomposition problem of the observed matrix, and several algorithms have been proposed to solve this. Direct exponential curve resolution algorithm (DECRA) is well used for DOSY analysis because DECRA is the only method to achieve a high analysis performance without using initial values. However, DECRA requires a high calculation cost depending on the size of the observed matrix. Then this paper proposes a new DOSY analysis method based on the difference approximation method and the eigenvalue decomposition. Based on the computational complexity, the numerical simulation, and an actual data analysis, this paper shows the efficiency of the proposed algorithm compared with DECRA.