Listing 1 - 4 of 4 |
Sort by
|
Choose an application
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
Banach spaces --- Parameter estimation --- Differential equations, Partial --- Banach, Espaces de --- Estimation d'un paramètre --- Equations aux dérivées partielles --- Banach spaces. --- Parameter estimation. --- Differential equations, Partial. --- Partial differential equations --- Estimation theory --- Stochastic systems --- Functions of complex variables --- Generalized spaces --- Topology --- Banach Space. --- Iterative Method. --- Regularization Theory. --- Tikhonov Regularization.
Choose an application
This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems.
Research & information: general --- Mathematics & science --- conservation laws --- feedback stabilization --- input-to-state stability --- numerical approximations --- nonlocal velocity --- macroscopic models --- traffic data --- gap analysis --- multi-phase models --- Volterra integral equations --- asymptotic-preserving --- numerical stability --- Cellular Potts model --- cell migration --- nucleus deformation --- microchannel device --- regularization theory --- multivariate stochastic processes --- cross-power spectrum --- magnetoencephalography --- MEG --- functional connectivity --- spectral complexity --- soil organic carbon --- RothC --- non-standard integrators --- Exponential Rosenbrock–Euler --- langevin equation --- Mean Field Games system --- kinetic Fokker–Planck equation --- hypoelliptic operators --- Caputo fractional derivative --- Allee effect --- existence and stability --- Hopf bifurcation --- implicit schemes --- optimal design --- soft tissue mechanics --- mutual information --- biaxial experiment --- inverse problems --- information theory --- LWR model --- follow-the-leader model --- phase transition --- creeping --- seepage --- fundamental diagram --- lane discipline --- networks --- aggregation equation --- relaxation limit --- scalar conservation law --- finite volume scheme --- differential equations --- mathematical biology --- microfluidic chip --- applied mathematics --- numerical methods --- computational mathematics --- differential and integro-differential models
Choose an application
This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems.
conservation laws --- feedback stabilization --- input-to-state stability --- numerical approximations --- nonlocal velocity --- macroscopic models --- traffic data --- gap analysis --- multi-phase models --- Volterra integral equations --- asymptotic-preserving --- numerical stability --- Cellular Potts model --- cell migration --- nucleus deformation --- microchannel device --- regularization theory --- multivariate stochastic processes --- cross-power spectrum --- magnetoencephalography --- MEG --- functional connectivity --- spectral complexity --- soil organic carbon --- RothC --- non-standard integrators --- Exponential Rosenbrock–Euler --- langevin equation --- Mean Field Games system --- kinetic Fokker–Planck equation --- hypoelliptic operators --- Caputo fractional derivative --- Allee effect --- existence and stability --- Hopf bifurcation --- implicit schemes --- optimal design --- soft tissue mechanics --- mutual information --- biaxial experiment --- inverse problems --- information theory --- LWR model --- follow-the-leader model --- phase transition --- creeping --- seepage --- fundamental diagram --- lane discipline --- networks --- aggregation equation --- relaxation limit --- scalar conservation law --- finite volume scheme --- differential equations --- mathematical biology --- microfluidic chip --- applied mathematics --- numerical methods --- computational mathematics --- differential and integro-differential models
Choose an application
This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems.
Research & information: general --- Mathematics & science --- conservation laws --- feedback stabilization --- input-to-state stability --- numerical approximations --- nonlocal velocity --- macroscopic models --- traffic data --- gap analysis --- multi-phase models --- Volterra integral equations --- asymptotic-preserving --- numerical stability --- Cellular Potts model --- cell migration --- nucleus deformation --- microchannel device --- regularization theory --- multivariate stochastic processes --- cross-power spectrum --- magnetoencephalography --- MEG --- functional connectivity --- spectral complexity --- soil organic carbon --- RothC --- non-standard integrators --- Exponential Rosenbrock–Euler --- langevin equation --- Mean Field Games system --- kinetic Fokker–Planck equation --- hypoelliptic operators --- Caputo fractional derivative --- Allee effect --- existence and stability --- Hopf bifurcation --- implicit schemes --- optimal design --- soft tissue mechanics --- mutual information --- biaxial experiment --- inverse problems --- information theory --- LWR model --- follow-the-leader model --- phase transition --- creeping --- seepage --- fundamental diagram --- lane discipline --- networks --- aggregation equation --- relaxation limit --- scalar conservation law --- finite volume scheme --- differential equations --- mathematical biology --- microfluidic chip --- applied mathematics --- numerical methods --- computational mathematics --- differential and integro-differential models --- conservation laws --- feedback stabilization --- input-to-state stability --- numerical approximations --- nonlocal velocity --- macroscopic models --- traffic data --- gap analysis --- multi-phase models --- Volterra integral equations --- asymptotic-preserving --- numerical stability --- Cellular Potts model --- cell migration --- nucleus deformation --- microchannel device --- regularization theory --- multivariate stochastic processes --- cross-power spectrum --- magnetoencephalography --- MEG --- functional connectivity --- spectral complexity --- soil organic carbon --- RothC --- non-standard integrators --- Exponential Rosenbrock–Euler --- langevin equation --- Mean Field Games system --- kinetic Fokker–Planck equation --- hypoelliptic operators --- Caputo fractional derivative --- Allee effect --- existence and stability --- Hopf bifurcation --- implicit schemes --- optimal design --- soft tissue mechanics --- mutual information --- biaxial experiment --- inverse problems --- information theory --- LWR model --- follow-the-leader model --- phase transition --- creeping --- seepage --- fundamental diagram --- lane discipline --- networks --- aggregation equation --- relaxation limit --- scalar conservation law --- finite volume scheme --- differential equations --- mathematical biology --- microfluidic chip --- applied mathematics --- numerical methods --- computational mathematics --- differential and integro-differential models
Listing 1 - 4 of 4 |
Sort by
|