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Abstract
Solving an autoconvolution equation is a nonlinear ill-posed inverse problem. Besides standard methods for general nonlinear problems several customized methods for deautoconvolution are available. Recently, a new decomposition approach for solving ill-posed quadratic equations, e.g. autoconvolutions, has been proposed. In this article we compare the new approach to the TIGRA method of Ramlau and to the local regularization method of Dai and Lamm. Numerical tests show that the new method yields better approximations to the unknown true solution than existing methods in comparable computation time.
Funding source: DFG
Award Identifier / Grant number: FL 832/1-1
Received: 2013-12-13
Revised: 2014-3-25
Accepted: 2014-4-1
Published Online: 2014-4-18
Published in Print: 2015-6-1
© 2015 by De Gruyter
