Verifying the Solution from a Nonlinear Solver - A Case Study: Reply

摘要

David M. Drakker and Vince Wiggins (2004; hereafter "DW") observed that the solutions to badly scaled and well-scaled versions of the model we analyzed in McCullough and Vinod (2003; hereafter "MV") are practically the same. Analyzing this phenomenon, DW revealed a lacuna in the prescription we offered (MV, Sec. El, subsection B) for analyzing the Hessian. DW called for further research on when the condition number is too high, and correctly indicated that there is a need for determining whether a high condition number "indicates a lack of identification that is inherent in the model and the data, and not something that can be easily fixed[.]" We have conducted the requisite research and can amend our prescription appropriately. We have seen in the literature numerous times the folk theorem that k digits of accuracy are lost in solving a linear system if the data matrix has condition number 10{sup}k. While it is easy to find the folk theorem, it is not so easy to find an important caveat under which the folk theorem might not hold.