23 August 1996 Ill-conditioning during damped least squares optimization of optical systems
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Abstract
Three methods have been investigated for detecting linear dependence between variables during damped least squares optimization. They are the angle (delta) between column vectors calculated from the scalar product, the normalized standard deviation of the ratios of corresponding elements and the singular values computed from a singular value decomposition. Optimization runs were made on a test lens where attempts were made to eliminate the causes of ill- conditioning by removing variables which were close to linear dependence. Results showed an improvement in the final merit function for all techniques with the exception of singular values. There was also a difference in the final solution forms which indicated that attempting to improve the conditioning of the matrix equations at source was advantageous for the test lens examined with forms closer to the optimum for the two successful techniques used for detecting linear dependence.
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Christopher C. Hull, Christopher C. Hull, } "Ill-conditioning during damped least squares optimization of optical systems", Proc. SPIE 2774, Design and Engineering of Optical Systems, (23 August 1996); doi: 10.1117/12.246704; https://doi.org/10.1117/12.246704
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