The convergence of the BenIsrael iteration for nonlinear least squares problems
Author:
Paul T. Boggs
Journal:
Math. Comp. 30 (1976), 512522
MSC:
Primary 65K05; Secondary 34D20
MathSciNet review:
0416018
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Abstract: BenIsrael [1] proposed a method for the solution of the nonlinear least squares problem where . This procedure takes the form where denotes the MoorePenrose generalized inverse of the Fréchet derivative of F. We give a general convergence theorem for the method based on Lyapunov stability theory for ordinary difference equations. In the case where there is a connected set of solution points, it is often of interest to determine the minimum norm least squares solution. We show that the BenIsrael iteration has no predisposition toward the minimum norm solution, but that any limit point of the sequence generated by the BenIsrael iteration is a least squares solution.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604160183
PII:
S 00255718(1976)04160183
Keywords:
BenIsrael iteration,
generalized inverses,
nonlinear least squares,
Lyapunov stability for difference equations
Article copyright:
© Copyright 1976 American Mathematical Society
