The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied ...The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in[4].In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in[4]and present the maximum entropy method for the Legendre moment problem.We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments,respectively,and utilizing the corresponding maximum entropy method.展开更多
We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known pa...We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known part of the boundary of a two-dimensional domain,for problems governed by Helmholtz-type equations.This inverse geometric problem is solved using the plane wavesmethod(PWM)in conjunction with the Tikhonov regularizationmethod.The value for the regularization parameter is chosen according toHansen’s L-curve criterion.The stability,convergence,accuracy and efficiency of the proposedmethod are investigated by considering several examples.展开更多
文摘The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in[4].In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in[4]and present the maximum entropy method for the Legendre moment problem.We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments,respectively,and utilizing the corresponding maximum entropy method.
文摘We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known part of the boundary of a two-dimensional domain,for problems governed by Helmholtz-type equations.This inverse geometric problem is solved using the plane wavesmethod(PWM)in conjunction with the Tikhonov regularizationmethod.The value for the regularization parameter is chosen according toHansen’s L-curve criterion.The stability,convergence,accuracy and efficiency of the proposedmethod are investigated by considering several examples.
