The Galerkin scheme for Lavrentiev's \(m\)-times iterated method to solve linear accretive Volterra integral equations of the first kind

DOI10.1007/BF02510220zbMath0882.65135MaRDI QIDQ1359975

Robert Plato

Publication date: 3 February 1998

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

algorithmconvergenceGalerkin methodregularizationill-posed problemsaccretive operatorsAbel's integral equationVolterra integral equations of first kindLavrentiev method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical methods for ill-posed problems for integral equations (65R30) Volterra integral equations (45D05)

Related Items (13)

A Discretizing Levenberg-Marquardt Scheme for Solving Nonlinear Ill-Posed Integral Equations ⋮ On the parameter choice in the multilevel augmentation method ⋮ Multilevel augmentation algorithms based on fast collocation methods for solving ill-posed integral equations ⋮ Regularization in a functional reproducing kernel Hilbert space ⋮ A parameter choice strategy for a multilevel augmentation method in iterated Lavrentiev regularization ⋮ Fast multiscale Galerkin methods for solving ill-posed integral equations via a coupled system under general source conditions ⋮ Fast multilevel augmentation methods with compression technique for solving ill-posed integral equations ⋮ Sparse discretization matrices for Volterra integral operators with applications to numerical differentiation ⋮ On Lavrentiev Regularization for Ill-Posed Problems in Hilbert Scales ⋮ A collocation method solving integral equation models for image restoration ⋮ Direct regularization for system of integral-algebraic equations of index-1 ⋮ A fast multiscale Galerkin method for the first kind ill‐posed integral equations via Tikhonov regularization ⋮ On optimal regularization methods for fractional differentiation

Cites Work

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• On Galerkin Methods for Abel-Type Integral Equations
• On pseudo—optimal parameter choices and stopping rules for regularization methods in banach spaces_∗
• Error bounds of discretization methods for boundary integral equations with noisy data
• Linear integral equations
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