Results 1  10
of
133,904
A SIMPLIFIED GENERALIZED GAUSSNEWTON METHOD FOR NONLINEAR ILLPOSED PROBLEMS
"... Abstract. Iterative regularization methods for nonlinear illposed equations of the form F(x) =y, whereF: D(F) ⊂ X → Y is an operator between Hilbert spaces X and Y, usually involve calculation of the Fréchet derivatives of F at each iterate and at the unknown solution x †. In this paper, we sugges ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
suggest a modified form of the generalized GaussNewton method which requires the Fréchet derivative of F only at an initial approximation x0 of the solution x †. The error analysis for this method is done under a general source condition which also involves the Fréchet derivative only at x0
A LEPSKIJTYPE STOPPINGRULE FOR SIMPLIFIED ITERATIVELY REGULARIZED GAUSSNEWTON METHOD
"... Abstract. Iterative regularization methods for nonlinear illposed equations of the form F (a) = y, where F: D(F) ⊂ X → Y is an operator between Hilbert spaces X and Y, usually involve calculation of the Fréchet derivatives of F at each iterate and at the unknown solution a ♯. A modified form of t ..."
Abstract
 Add to MetaCart
of the generalized GaussNewton method which requires the Fréchet derivative of F only at an initial approximation a0 of the solution a ♯ as studied by Mahale and Nair [11]. This work studied an a posteriori stopping rule of Lepskijtype of the method. A numerical experiment from inverse source potential problem
Convergence and uniqueness properties of GaussNewton’s method
 Comput. Math. Appl
"... Abst ractThe generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of GaussNewton's method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of GaussNewton's method and th ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Abst ractThe generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of GaussNewton's method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of GaussNewton's method
Convergence analysis of a proximal GaussNewton method
, 2011
"... Abstract An extension of the GaussNewton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applicat ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract An extension of the GaussNewton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some
A note on the convergence of GaussNewton algorithm
"... Introduction The Nonlinear Least Squares Problem (NLSP) min x kF (x)k 2 ; (1) where F : R n 7! R m is a nonlinear function, and k:k 2 denotes the Euclidean norm, can generally be solved only by iteratives methods. It arises in the framework of data fitting problems. Suppose, for example, th ..."
Abstract
 Add to MetaCart
Introduction The Nonlinear Least Squares Problem (NLSP) min x kF (x)k 2 ; (1) where F : R n 7! R m is a nonlinear function, and k:k 2 denotes the Euclidean norm, can generally be solved only by iteratives methods. It arises in the framework of data fitting problems. Suppose, for example
General methods for monitoring convergence of iterative simulations
 J. Comput. Graph. Statist
, 1998
"... We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develo ..."
Abstract

Cited by 551 (8 self)
 Add to MetaCart
We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order
A continuation method for the efficient solution of parametric optimization problems in kinetic model reduction. arXiv:1301.5815
, 2013
"... Abstract. Model reduction methods often aim at an identification of slow invariant manifolds in the state space of dynamical systems modeled by ordinary differential equations. We present a predictor corrector method for a fast solution of an optimization problem the solution of which is supposed to ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
to approximate points on slow invariant manifolds. The corrector method is either an interior point method or a generalized Gauss–Newton method. The predictor is an Euler prediction based on the parameter sensitivities of the optimization problem. The benefit of a step size strategy in the predictor corrector
Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization
, 1993
"... The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to a ..."
Abstract

Cited by 633 (15 self)
 Add to MetaCart
The paper describes a rankbased fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified
Multipoint quantitativetrait linkage analysis in general pedigrees
 Am. J. Hum. Genet
, 1998
"... Multipoint linkage analysis of quantitativetrait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variancecomponent linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint i ..."
Abstract

Cited by 567 (60 self)
 Add to MetaCart
Multipoint linkage analysis of quantitativetrait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variancecomponent linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint
Results 1  10
of
133,904