CORRIGENDUM: A new Abel inversion by means of the integrals of an input function with noise

Abel’s integral equations arise in many areas of natural science and engineering, particularly in plasma diagnostics. This paper proposes a new and effective approximation of the inversion of Abel transform. This algorithm can be simply implemented by symbolic computation, and moreover an nth-order approximation reduces to the exact solution when it is a polynomial in r 2 of degree less than or equal to n. Approximate Abel inversion is expressed in terms of integrals of input measurement data; so the suggested approach is stable for experimental data with random noise. An error analysis of the approximation of Abel inversion is given. Finally, several test examples used frequently in plasma diagnostics are given to illustrate the effectiveness and stability of this method.

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