Updating the qr factorization and the least squares problem

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While this method has great intuitive appeal, and very long tradition, numerical analysts in other problem domains usually use other methods.The condition number of the matrix is a measure of the amount of significance lost when you solve the system it represents.For the same reason the presentation will be in terms of an upper triangular matrix, even though a lower triangular matrix is somewhat more natural to the problem.Instead of full three dimensional adjustments, level nets will be used in order to simplify this presentation.

The problem has been linearized, converting the shots into changes in coordinates.When the ratio of redundant shots to non-redundant shots is small Network adjustment problems are usually set up as a (linearized) weighted matrix problem.The least squares solution of this problem is usually computed by "the method of normal equations".Researching this on the web, I am having a difficult time finding information since I don't know what this method would be called.© Copyright 2001, by American Congress on Surveying and Mapping, All Rights Reserved. This peer reviewed paper appeared in the June 2001 Issue of Surveying and Land Information Systems The equations and diagrams here are ASCII art, since I don't think that the typeset equations are THAT much more readable, and I don't normally put in graphics unless there are significant improvements in readability.

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