病态总体最小二乘问题的谱修正迭代法

针对病态问题岭估计法及正则化方法存在破坏方程的等量关系、解是有偏估计的问题,在最小二乘谱修正迭代法的基础上,提出病态总体最小二乘问题的谱修正迭代法,并推导了总体最小二乘谱修正迭代法及其改进算法的具体公式。通过算例验证和阐明了TLS谱修正迭代法在病态问题中的有效性和易受迭代初值影响的缺点。

Iteration Method by Correcting Characteristic Values to Ill-posed Total Least Squares Problem

The ridge estimation and regularization methods are deficient because they destroy the equivalence relationship of the equation and the solution is a biased estimation. To overcome these deficiencies, an iteration method of correcting characteristic values to TLS, and its improved algorithm, are proposed on the basis of the iteration method, by correcting characteristic values to LS. The results of the examples show that the iteration method of correcting characteristic values to TLS or LS is equivalent to the general TLS or LS respectively in normal situations, and the algorithms proposed are effective but susceptible to the initial iteration value in ill-conditioned situations.