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A regularization procedure for the auto‐correlation equation
Author(s) -
Von Wolfersdorf L.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.257
Subject(s) - mathematics , regularization (linguistics) , quadratic equation , mathematical analysis , fourier transform , integral equation , boundary value problem , convergence (economics) , geometry , artificial intelligence , computer science , economics , economic growth
The paper deals with the auto‐correlation equation and its regularization by means of a Lavrent'ev regularization procedure in L 2 . The solution of this quadratic integral equation of the first kind and of the regularized equation of the second kind are obtained by reduction to a boundary value problem for the Fourier transform of the solution. We prove convergence of the approximate solution to the exact solution and derive a stability estimate for the error. Copyright © John Wiley & Sons, Ltd.