Stable solutions of some ill‐posed problems

DOI10.1002/mma.1670030125zbMath0469.65034OpenAlexW2013552717MaRDI QIDQ3923520

Alexander G. Ramm

Publication date: 1981

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1670030125

zbMATH Keywords

ill-posed problemiterative processescharacteristic valuestable solutions

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Abstract integral equations, integral equations in abstract spaces (45N05) Theoretical approximation of solutions to integral equations (45L05) Integral, integro-differential, and pseudodifferential operators (47Gxx)

Related Items (16)

Numerical recovery of the layered medium from the surface data ⋮ Remarks about inverse diffraction problem ⋮ Calculating singular integrals as an ill-posed problem ⋮ Is the Born approximation good for solving the inverse problem when the potential is small? ⋮ On stable numerical differentiation ⋮ Dynamical systems method for solving operator equations. ⋮ Inversion of limited-angle tomographic data ⋮ On deconvolution methods ⋮ On deconvolution problems: numerical aspects ⋮ General explicit difference formulas for numerical differentiation ⋮ On a new notion of the solution to an ill-posed problem ⋮ Numerical inversion of the Laplace transform from the real axis ⋮ Estimates of derivatives of random functions. I ⋮ Reconstructing singularities of a function from its Radon transform ⋮ Estimates of derivatives of random functions. II ⋮ On the inverse diffraction problem

Cites Work

• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• On Simultaneous Approximation of a Function and its Derivative by Interpolation Polynomials
• Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
• Least Squares Methods for Ill-Posed Problems with a Prescribed Bound
• An Iteration Formula for Fredholm Integral Equations of the First Kind
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