OPTIMAL ERROR BOUND AND APPROXIMATION METHODS FOR A CAUCHY PROBLEM OF THE MODIFIED HELMHOLTZ EQUATION

DOI10.1142/S0219691311004080zbMath1218.35252MaRDI QIDQ3007754

Yu-Jiang Wu, Ailin Qian

Publication date: 17 June 2011

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

zbMATH Keywords

error estimateTikhonov regularizationill-posed problemsmodified Helmholtz equationspectral regularization

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Cites Work

• Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation
• Numerical solution of a Cauchy problem for the Laplace equation
• Determining Surface Temperatures from Interior Observations
• Optimality for ill-posed problems under general source conditions
• Geometry of linear ill-posed problems in variable Hilbert scales
• Approximate solution of a Cauchy problem for the Helmholtz equation