On Computing a Stable Least Squares Solution to the Inverse Problem for a Planar Newtonian Potential

1971 ◽  
Vol 20 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Hrair S. Cabayan ◽  
Geneva G. Belford
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Newtonian Potential ◽  
Least Squares Solution

scholarly journals MODAL INVERSION BY USING PARAMETERIZATION WITH CHEBYSHEV POLYNOMIALS

2016 ◽  
Vol 34 (3) ◽  
Author(s):  
Fernando De Oliveira Marin ◽  
Orlando Camargo Rodríguez ◽  
Luiz Gallisa Guimarães ◽  
Carlos Eduardo Parente Ribeiro
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Shallow Water ◽  
Chebyshev Polynomials ◽  
Sound Speed ◽  
Fundamental Importance ◽  
Model Parameters ◽  
Travel Times ◽  
Orthogonal Functions ◽  
Least Squares Solution

ABSTRACT. This paper discusses the estimation of sound speed perturbations in a shallow water waveguide, from measurements of modal travel times. The formulation of the Inverse Problem is reduced to a least squares solution, being highlighted that the choice of discretization of the set of model parameters is of fundamental importance. In the...Keywords: shallow water, tomography, orthogonal functions. RESUMO. Este trabalho aborda a estimativa de perturbações de velocidade do som em um ambiente de águas rasas, a partir de medições de tempo de percurso modal. A formulação do Problema Inverso é reduzida a uma solução por mínimos quadrados, sendo destacado que a escolha da discretização do conjunto de parâmetros do modelo é de fundamental...Palavras-chave: águas rasas, tomografia, funções ortogonais.

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

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