ISSN:
1573-2878
Keywords:
Secant method
;
quasi-Newton methods
;
least squares
;
superlinear convergence
;
bounded deterioration
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In 1981, Dennis and Walker developed a convergence theory for structured secant methods which included the PSB and the DFP secant methods but not the straightforward structured version of the BFGS secant method. Here, we fill this gap in the theory by establishing a convergence theory for the structured BFGS secant method. A direct application of our new theory gives the first proof of local andq-superlinear convergence of the important structured BFGS secant method for the nonlinear least-squares problem, which is used by Dennis, Gay, and Welsh in the current version of the popular and successful NL2SOL code.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00962795
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