scholarly journals A Banach Space Regularization Approach for Multifrequency Microwave Imaging

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Claudio Estatico ◽  
Alessandro Fedeli ◽  
Matteo Pastorino ◽  
Andrea Randazzo
Keyword(s):  
Banach Space ◽  
Data Processing ◽  
Numerical Simulations ◽  
Banach Spaces ◽  
Newton Method ◽  
Mathematical Formulation ◽  
Processing Technique ◽  
Microwave Imaging ◽  
Inexact Newton Method ◽  
Reconstruction Method

A method for microwave imaging of dielectric targets is proposed. It is based on a tomographic approach in which the field scattered by an unknown target (and collected in a proper observation domain) is inverted by using an inexact-Newton method developed inLpBanach spaces. In particular, the extension of the approach to multifrequency data processing is reported. The mathematical formulation of the new method is described and the results of numerical simulations are reported and discussed, analyzing the behavior of the multifrequency processing technique combined with the Banach spaces reconstruction method.

scholarly journals The Ivanov regularized Gauss–Newton method in Banach space with an a posteriori choice of the regularization radius

2019 ◽  
Vol 27 (4) ◽  
pp. 539-557
Author(s):  
Barbara Kaltenbacher ◽  
Andrej Klassen ◽  
Mario Luiz Previatti de Souza
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Newton Method ◽  
Noise Level ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
A Priori ◽  
Discrepancy Principle ◽  
A Posteriori ◽  
Source Condition

Abstract In this paper, we consider the iteratively regularized Gauss–Newton method, where regularization is achieved by Ivanov regularization, i.e., by imposing a priori constraints on the solution. We propose an a posteriori choice of the regularization radius, based on an inexact Newton/discrepancy principle approach, prove convergence and convergence rates under a variational source condition as the noise level tends to zero and provide an analysis of the discretization error. Our results are valid in general, possibly nonreflexive Banach spaces, including, e.g., {L^{\infty}} as a preimage space. The theoretical findings are illustrated by numerical experiments.

scholarly journals Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Zdeněk Šmarda ◽  
Yasir Khan ◽  
Qingbiao Wu
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Banach Spaces ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Convergence Theorem ◽  
Order Convergence ◽  
Third Order ◽  
The Third

Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.

GROUP THEORETICAL APPROACH TO QUANTUM ENTANGLEMENT AND TOMOGRAPHY WITH WAVELET TRANSFORM IN BANACH SPACES

2007 ◽  
Vol 05 (03) ◽  
pp. 367-386 ◽  
Author(s):  
M. REZAEE ◽  
M. A. JAFARIZADEH ◽  
M. MIRZAEE
Keyword(s):  
Banach Space ◽  
Wavelet Transform ◽  
Banach Spaces ◽  
Theoretical Approach ◽  
Unitary Group ◽  
Atomic Decomposition ◽  
Rotation Group ◽  
Reconstruction Method ◽  
Banach Frame ◽  
Separability Criteria

The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and some of well-known quantum tomographies, such as tomography of rotation group, spinor tomography and tomography of unitary group, is established. Also both the atomic decomposition and Banach frame nature of these quantum tomographic examples are revealed in detail. Finally, we consider separability criteria for any state with group theoretical wavelet transform on Banach spaces.

scholarly journals AN INEXACT NEWTON METHOD WITH INNER PRECONDITIONED CG FOR NON-UNIFORMLY MONOTONE ELLIPTIC PROBLEMS

2021 ◽  
Vol 26 (3) ◽  
pp. 383-394
Author(s):  
Benjámin Borsos
Keyword(s):  
Banach Space ◽  
Newton Method ◽  
Lower Bounds ◽  
Numerical Experiments ◽  
Real Life ◽  
Elliptic Problems ◽  
Upper And Lower Bounds ◽  
Preconditioned Conjugate Gradient ◽  
Inexact Newton Method ◽  
Convergence Results

The present paper introduces an inexact Newton method, coupled with a preconditioned conjugate gradient method in inner iterations, for elliptic operators with non-uniformly monotone upper and lower bounds. Convergence is proved in Banach space level. The results cover real-life classes of elliptic problems. Numerical experiments reinforce the convergence results.

A Multifrequency Inexact-Newton Method in ${L^p}$ Banach Spaces for Buried Objects Detection

2015 ◽  
Vol 63 (9) ◽  
pp. 4198-4204 ◽  
Author(s):  
Claudio Estatico ◽  
Alessandro Fedeli ◽  
Matteo Pastorino ◽  
Andrea Randazzo
Keyword(s):  
Banach Spaces ◽  
Newton Method ◽  
Inexact Newton Method ◽  
Content Type ◽  
Buried Objects ◽  
Objects Detection
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