Entropy- and Tikhonov-based regularization techniques applied to the backwards heat equation

DOI10.1016/S0898-1221(00)85017-8zbMath1016.80016OpenAlexW2032718614MaRDI QIDQ1591936

Haroldo Fraga de Campos Velho, Fernando Manuel Ramos, Wagner Barbosa Muniz

Publication date: 14 January 2001

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(00)85017-8

zbMATH Keywords

regularizationinverse problemsmaximum entropy principleTikhonov regularizationtruncated singular value decompositioninverse heat conduction problemMorozov's discrepancy principlebackwards heat equation

Mathematics Subject Classification ID

Related Items (23)

Global field interpolation for particle methods ⋮ A vectorial descent stepsize for parameter identification of a coupled parabolic PDE-ODE ⋮ A new algorithm for direct and backward problems of heat conduction equation ⋮ Two stable methods with numerical experiments for solving the backward heat equation ⋮ Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations ⋮ Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem ⋮ Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm ⋮ A new operational matrix method based on the Bernstein polynomials for solving the backward inverse heat conduction problems ⋮ Optimal algorithms in a Krylov subspace for solving linear inverse problems by MFS ⋮ Numerical computation for backward time-fractional diffusion equation ⋮ Epidemic Genetic Algorithm for Solving Inverse Problems: Parallel Algorithms ⋮ Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison ⋮ An a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems ⋮ A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data ⋮ On an inverse problem: recovery of non-smooth solutions to backward heat equation ⋮ Regularization of the backward-in-time Kuramoto-Sivashinsky equation ⋮ Fundamental kernel-based method for backward space-time fractional diffusion problem ⋮ Numerical solution of three-dimensional backward heat conduction problems by the time evolution method of fundamental solutions ⋮ Inverse reconstruction of initial and boundary conditions of a heat transfer problem with accurate final state ⋮ A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data ⋮ Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework ⋮ The backward group preserving scheme for 1D backward in time advection-dispersion equation ⋮ Analytic series solutions of 2D forward and backward heat conduction problems in rectangles and a new regularization

Uses Software

• nag

Cites Work

• Solution of a multidimensional heat conduction inverse problem using the finite analytic method and the principle of maximum entropy
• Information Theory and Statistical Mechanics
• Novel approaches to entropic regularization
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