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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1007/s00194-015-0043-4

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0945-3245

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Multiparameter regularization and its numerical r

Authors: Shuai Lu Sergei V Pereverzev
Publish Date: 2010/07/03
Volume: 118, Issue: 1, Pages: 1-31
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Abstract

In this paper we propose and analyse a choice of parameters in the multiparameter regularization of Tikhonov type A modified discrepancy principle is presented within the multiparameter regularization framework An order optimal error bound is obtained under the standard smoothness assumptions We also propose a numerical realization of the multiparameter discrepancy principle based on the model function approximation Numerical experiments on a series of test problems support theoretical results Finally we show how the proposed approach can be successfully implemented in Laplacian Regularized Least Squares for learning from labeled and unlabeled examples

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Other Papers In This Journal:
  1. Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
  2. A new class of symplectic integration schemes based on generating functions
  3. An optimal adaptive finite element method for elastoplasticity
  4. Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
  5. Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain
  6. Decay rates of adaptive finite elements with Dörfler marking
  7. Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes
  8. Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
  9. A uniformly stable Fortin operator for the Taylor–Hood element
  10. A locking-free $$hp$$ DPG method for linear elasticity with symmetric stresses
  11. Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
  12. The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem
  13. Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
  14. Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization
  15. Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods
  16. A residual–based error estimator for BEM–discretizations of contact problems
  17. An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems
  18. Preconditioners for pseudodifferential equations on the sphere with radial basis functions
  19. Symmetric multistep methods for constrained Hamiltonian systems
  20. Discrete minimum and maximum principles for finite element approximations of non-monotone elliptic equations
  21. Numerical Eulerian method for linearized gas dynamics in the high frequency regime
  22. Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
  23. The boundary element spline collocation for nonuniform meshes on the torus
  24. Delay-dependent stability of high order Runge–Kutta methods
  25. Intrinsic finite element methods for the computation of fluxes for Poisson’s equation
  26. On generalized successive overrelaxation methods for augmented linear systems
  27. On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
  28. A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate
  29. Intrinsic representation of tangent vectors and vector transports on matrix manifolds
  30. Crouzeix–Raviart boundary elements
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