Multiparameter regularization for Volterra kernel identification via multiscale collocation methods

DOI10.1007/S10444-008-9077-4zbMath1190.65200OpenAlexW2087863136MaRDI QIDQ1047135

Yuesheng Xu, Marty Brenner, Ying Jiang

Publication date: 4 January 2010

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-008-9077-4

zbMATH Keywords

collocation methodnumerical resultsinverse problemmultiscalingmultiparameter regularizationVolterra kernel identificationnumerical quadrature strategy

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical methods for ill-posed problems for integral equations (65R30) Volterra integral equations (45D05) Numerical methods for inverse problems for integral equations (65R32) Linear operators and ill-posed problems, regularization (47A52) Inverse problems for integral equations (45Q05)

Related Items (4)

Sparse Deep Neural Network for Nonlinear Partial Differential Equations ⋮ Kernel‐based regularization least squares algorithm for nonlinear time‐delayed systems using self‐organizing maps ⋮ Multilevel augmentation algorithms based on fast collocation methods for solving ill-posed integral equations ⋮ Joint Inversion of Multiple Observations

Cites Work

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• Derivative corrections for quadrature formulas
• Reconstruction and decomposition algorithms for biorthogonal multiwavelets
• Multi-parameter regularization method for atmospheric remote sensing
• Superconvergence of piecewise polynomial Galerkin approximations, for Fredholm integral equations of the second kind
• A construction of refinable sets for interpolating wavelets
• Variable order composite quadrature of singular and nearly singular integrals
• Using the matrix refinement equation for the construction of wavelets on invariant sets
• Wavelet Galerkin methods for second-kind integral equations
• Multi-parameter regularization techniques for ill-conditioned linear systems
• A factorization method for identification of Volterra systems
• Limit values of derivatives of the Cauchy integrals and computation of the logarithmic potentials
• Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models
• Nonlinear model-based control using second-order Volterra models
• Fast collocation methods for high-dimensional weakly singular integral equations
• Fast numerical collocation solutions of integral equations
• A fast wavelet collocation method for integral equations on polygons
• Shadow block iteration for solving linear systems obtained from wavelet transforms
• Efficient algorithms for Volterra system identification
• Efficient determination of multiple regularization parameters in a generalized L-curve framework
• A multilevel augmentation method for solving ill-posed operator equations
• Piecewise Continuous Collocation for Integral Equations
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• A construction of interpolating wavelets on invariant sets
• Gauss-Type Quadratures for Weakly Singular Integrals and their Application to Fredholm Integral Equations of the Second Kind
• Fast Collocation Methods for Second Kind Integral Equations
• Multi-Parameter Regularization Methods for High-Resolution Image Reconstruction With Displacement Errors
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• An Introduction to Partial Differential Equations
• Volterra Kernel Identification Using Triangular Wavelets

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