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Truncated Regularized Solution to Ill-Posed Model and ItsUnbiased Estimation of Unit Weighted Variance" />
The regularized method improves the ill-posedness of the normal matrix by introducing the regularized parameter to correct the singular values. However, it is obviously unreasonable to correct the singular values without distinction. In this paper, we compare the trajectory decomposition expansions of the regularized mean square error and the least squares solution variance, analyze the relationship between the change of the mean square error of the solution caused by the modified singular value and the singular value, and determine the conditions for singular value correction. Based on the residual quadratic expectation formula, an error calculation formula for unbiased unit weights with improved regularization is derived. Finally, numerical examples and ill-trimmed network examples are used to verify the correctness of the formula."/>
<div style="line-height: 150%">Truncated Regularized Solution to Ill-Posed Model and ItsUnbiased Estimation of Unit Weighted Variance</div>
Abstract The regularized method improves the ill-posedness of the normal matrix by introducing the regularized parameter to correct the singular values. However, it is obviously unreasonable to correct the singular values without distinction. In this paper, we compare the trajectory decomposition expansions of the regularized mean square error and the least squares solution variance, analyze the relationship between the change of the mean square error of the solution caused by the modified singular value and the singular value, and determine the conditions for singular value correction. Based on the residual quadratic expectation formula, an error calculation formula for unbiased unit weights with improved regularization is derived. Finally, numerical examples and ill-trimmed network examples are used to verify the correctness of the formula.
