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SVD, Transformations, and the Search for a Better Minimum

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Abstract

Singular Value Decomposition (SVD) is the method of choice for solving ill-conditioned systems of linear This paper will give geometrical interpretations of SVD as applied to the problem of optical design. Although these interpretations suggest an orthogonalization of variables and defects, we will show that such orthogonalization is not appropriate for most optical design problems. A simplified set of transformations, however, does provide insight on some of the classic problems of lens design. Finally, we will present some current work on curvilinear “valley” following methods and show their application to optical design.

© 1994 Optical Society of America

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