Fast multilevel augmentation methods with compression technique for solving ill-posed integral equations

DOI10.1216/JIE-2011-23-1-39zbMath1229.65233MaRDI QIDQ548792

Zhongying Chen, Sirui Cheng, Hong-qi Yang

Publication date: 30 June 2011

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

numerical resultsinverse problemprojection methodoptimal error estimatesill-posed problemmatrix compressiona posteriori parameter choiceLavrentiev regularizationlinear, positive semidefinite integral operatormultilevel augmentation method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05) Numerical methods for inverse problems for integral equations (65R32) Linear integral equations (45A05)

Related Items (4)

A fast multilevel iteration method for solving linear ill-posed integral equations ⋮ Heuristic parameter choice rule for solving linear ill-posed integral equations in finite dimensional space ⋮ A parameter choice strategy for a multilevel augmentation method in iterated Lavrentiev regularization ⋮ Adaptive multilevel iteration methods for solving ill-posed integral equations via a coupled system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cascadic multilevel methods for ill-posed problems
• Multilevel algorithms for ill-posed problems
• Using the matrix refinement equation for the construction of wavelets on invariant sets
• A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization
• The Galerkin scheme for Lavrentiev's \(m\)-times iterated method to solve linear accretive Volterra integral equations of the first kind
• Wavelet Galerkin methods for second-kind integral equations
• Self-regularization by projection for noisy pseudodifferential equations of negative order
• Subspace preconditioned LSQR for discrete ill-posed problems
• Multigrid preconditioning and Toeplitz matrices
• Two-level preconditioners for regularized inverse problems. I: Theory
• Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
• On the regularizing properties of a full multigrid method for ill-posed problems
• Fast wavelet transforms and numerical algorithms I
• A multilevel augmentation method for solving ill-posed operator equations
• Fast collocation methods for solving ill-posed integral equations of the first kind
• A construction of interpolating wavelets on invariant sets
• Fast Collocation Methods for Second Kind Integral Equations
• Wavelet-Galerkin methods for ill-posed problems
• A fast multiscale Galerkin method for the first kind ill‐posed integral equations via Tikhonov regularization
• An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
• A multilevel method for solving operator equations

This page was built for publication: Fast multilevel augmentation methods with compression technique for solving ill-posed integral equations