一种改进的不适定问题奇异值分解法

An Improved Singular Values Decomposition Method for Ill-Posed Problem

综合截断奇异值法和奇异值修正法的特点,提出了一种改进的不适定问题奇异值分解法,先用截断参数将奇异值分为相对较大的奇异值和相对较小的奇异值;再用修正参数对相对较小的奇异值进行修正,以抑制其对观测噪声的放大作用。通过位场延拓中航空重力测量数据向下延拓的仿真实验,验证了改进的奇异值分解法要优于截断奇异值法、奇异值修正法和Tikhonov正则化法。

Based on the characteristics of the truncation singular values method and the modification singular values method,an improved singular values decomposition method is designed.The basic principle of the method is synchronously using the truncation parameter and the modification parameter to deal with the singular values of the coefficient matrix.The simulational results from the downward continuation of the airborne gravity data show that the significant quality advantages of the improved singular values decomposition method.