All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 19 of 19

Showing per page

A discrepancy principle for Tikhonov regularization with approximately specified data

M. Thamban Nair, Eberhard Schock (1998)

Annales Polonici Mathematici

Many discrepancy principles are known for choosing the parameter α in the regularized operator equation ( T * T + α I ) x α δ = T * y δ , | y - y δ | ≤ δ , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and T * y δ are approximated by Aₙ and z ₙ δ respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable...

An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

Nikolay Koshev, Larisa Beilina (2013)

Open Mathematics

We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally...

Dynamical systems method for solving linear finite-rank operator equations

N. S. Hoang, A. G. Ramm (2009)

Annales Polonici Mathematici

A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.

Dynamical systems method for solving linear ill-posed problems

A. G. Ramm (2009)

Annales Polonici Mathematici

Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning the discrepancy principle for choosing the regularization parameter are obtained.

Exponential convergence of hp quadrature for integral operators with Gevrey kernels

Alexey Chernov, Tobias von Petersdorff, Christoph Schwab (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Galerkin discretizations of integral equations in ℝ d require the evaluation of integrals I = ∫ S ( 1 ) ∫ S ( 2 ) g ( x , y ) d y d x where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for x ≠ y and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules 𝒬 N using N function evaluations of g which achieves exponential convergence |I – 𝒬 N | ≤C exp(–rNγ) with...

Exponential convergence of hp quadrature for integral operators with Gevrey kernels

Alexey Chernov, Tobias von Petersdorff, Christoph Schwab (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Galerkin discretizations of integral equations in ℝ d require the evaluation of integrals I = ∫ S ( 1 ) ∫ S ( 2 ) g ( x , y ) d y d x where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for x ≠ y and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules 𝒬 N using N function evaluations of g which achieves exponential convergence |I – 𝒬 N | ≤C exp(–rNγ) with...

Minimax and bayes estimation in deconvolution problem*

Mikhail Ermakov (2008)

ESAIM: Probability and Statistics

We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function εh where h ∈ L2(R1) and ε is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

Currently displaying 1 – 19 of 19

Page 1