An Adaptive Nonlinear Least Square Algorithm
John E. Dennis, David M. Gay, Roy E. Welsch
NBER Working Paper No. 196
NL2SOL is a modular program for solving the nonlinear least-squares problem that incorporates a number of novel features. It maintains a secant approximation S to the second-order part of the least-squares Hessian and adaptively decides when to use this approximation. We have found it very helpful to "size" S before updating it, something which looks much akin to Oren-Luenberger scaling. Rather than resorting to line searches or Levenberg-Marquardt modifications, we use the double-dogleg scheme of Dennis and Mei together with a special module for assessing the quality of the step thus computed. We discuss these and other ideas behind NLZSOL and briefly describe its evolution and current implementation.
Document Object Identifier (DOI): 10.3386/w0196
Published: John E. Dennis & David M. Gay & Roy E. Walsh, 1981. "An Adaptive Nonlinear Least-Squares Algorithm," ACM Transactions on Mathematical Software, vol 7(3), pages 348-368.
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