105 citations · 736 across the 32 of their papers we have counts for
32 papers
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 the value function for nonautonomous optimal control problems with infinite horizon
J. Baumeister, A. Leitao, G. N. Silva
In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by -functions. We verify that the value function is…
Regularization by dynamic programming
S. Kindermann, A. Leitao
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadra…
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…
Semiconductors and Dirichlet-to-Neumann maps
A. Leitao
We investigate the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by the stationary voltage-current (VC) map. The related inverse…
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…
Optimal exploitation of renewable resource stocks: Necessary conditions
J. Baumeister, A. Leitao
We study a model for the exploitation of renewable stocks developed in Clark et al. (Econometrica 47 (1979), 25-47). In this particular control problem, the control law contains a…
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…
On inverse doping profile problems for the stationary voltage-current map
A. Leitao, P. A. Markowich, J. P. Zubelli
We consider the problem of identifying possibly discontinuous doping profiles in semiconductor devices from data obtained by\,stationary voltage-current maps. In particular, we foc…
On inverse problems for semiconductor equations
M. Burger, H. W. Engl, A. Leitão +1
This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several id…
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.…