105 citations · 736 across the 32 of their papers we have counts for
25 papers · 1 filter
On level set type methods for elliptic Cauchy problems
A. Leitao, M. Marques Alves
Two methods of level set type are proposed for solving the Cauchy problem for an elliptic equation. Convergence and stability results for both methods are proven, characterizing th…
On regularization methods based on dynamic programming techniques
S. Kindermann, A. Leitao
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization m…
On regularization methods for inverse problems of dynamic type
S. Kindermann, A. Leitao
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic opt…
Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
J. Baumeister, A. De Cezaro, A. Leitao
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the prop…
On the identification of piecewise constant coefficients in optical diffusion tomography by level set
J. P. Agnelli, A. De Cezaro, A. Leitao +1
In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coef…
On Tikhonov functionals penalized by Bregman distances
I. R. Bleyer, A. Leitao
We investigate Tikhonov regularization methods for nonlinear ill-posed problems in Banach spaces, where the penalty term is described by Bregman distances. We prove convergence and…
Iterative regularization methods for a discrete inverse problem in MRI
A. Leitao, J. Zubelli
We propose and investigate efficient numerical methods for inverse problems related to Magnetic Resonance Imaging (MRI). Our goal is to extend the recent convergence results for th…
On inverse problems modeled by PDE's
A. Leitao
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent…
Mean value methods for solving the heat equation backwards in time
A. Leitao
We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite th…
On iterative methods for solving ill-posed problems modeled by PDE's
J. Baumeister, A. Leitao
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider…
An iterative method for solving elliptic Cauchy problems
A. Leitao
We investigate the Cauchy problem for elliptic operators with -coefficients at a regular set , which is a classical example of an ill-posed problem. The Cau…
Applications of the Backus-Gilbert method to linear and some non linear equations
A. Leitao
We investigate the use of a functional analytical version of the Backus-Gilbert Method as a reconstruction strategy to get specific information about the solution of linear and sli…
Inverse problems for semiconductors: models and methods
A. Leitao, P. A. Markowich, J. P. Zubelli
We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationar…
Regularization of systems of nonlinear ill-posed equations: II. Applications
M. Haltmeier, R. Kowar, A. Leitao +1
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem r…
Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
M. Haltmeier, A. Leitao, O. Scherzer
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in…
On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations
J. Baumeister, B. Kaltenbacher, A. Leitao
In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations is invest…
Mean value iterations for nonlinear elliptic Cauchy problems
P. Kügler, A. Leitao
We investigate the Cauchy problem for a class of nonlinear elliptic operators with -coefficients at a regular set . The Cauchy data are given at a manifold…
A Mann iterative regularization method for elliptic Cauchy problems
H. W. Engl, A. Leitao
We investigate the Cauchy problem for linear elliptic operators with -coefficients at a regular set , which is a classical example of an ill-posed problem.…
Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators
F. Frühauf, O. Scherzer, A. Leitao
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular ap…
On a family of gradient type projection methods for nonlinear ill-posed problems
A. Leitao, B. F. Svaiter
We propose and analyze a family of successive projection methods whose step direction is the same as Landweber method for solving nonlinear ill-posed problems that satisfy the Tang…
Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg-Marquardt method
A. Leitao, F. Margotti, B. F. Svaiter
In this article we propose a novel strategy for choosing the Lagrange multipliers in the Levenberg-Marquardt method for solving ill-posed problems modeled by nonlinear operators ac…
On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations
A. Leitao, B. F. Svaiter
In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The unde…
Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method
R. Boiger, A. Leitao, B. F. Svaiter
In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear op…
A Computational Approach for the inverse problem of neuronal conductances determination
Jemy A. Mandujano Valle, Alexandre L. Madureira, Antonio Leitão
The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using neurons of the giant squid. It becomes clear…