IJPAM: Volume 2, No. 1 (2002)

CONTINUOUS REGULARIZED GAUSS-NEWTON-TYPE
ALGORITHM FOR NONLINEAR ILL-POSED
EQUATIONS WITH SIMULTANEOUS UPDATES OF
INVERSE DERIVATIVE

Alexander G. Ramm$^1$, Alexandra B. Smirnova$^2$
$^1$Dept of Mathematics
Kansas State University
Manhattan, KS 66506, USA
e-mail: ramm@math.ksu.edu
$^2$Dept. of Mathematics and Statistics
Georgia State University
Atlanta, GA 30303, USA
e-mail: smirn@cs.gsu.edu


Abstract.A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $[F^{\pr*}(x(t))F'(x(t))+\ep(t) I]^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is proved. An attractive and novel feature of the proposed method is the absence of assumptions about the location of the spectrum of operator $F'(x)$. The absence of such assumptions is made possible by a source-type condition.

Received: January 13, 2002

AMS Subject Classification: 65J15, 58C15, 47H17

Key Words and Phrases: nonlinear ill-posed problems, continuous regularization, integral inequality, Fréchet derivative, Gauss-Newton's method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 1