An improved model function method for choosing regularization parameters in linear inverse problems

By Jianli Xie, Jun Zou. 2002

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On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales (2009, methodology): “…to noise, it is customary to use a “regularization" method to solve this sort of ill-posed problem [Kunisch and Zou (1998); Wang and Xiao (2001); Xie and Zou (2002); Resmerita (2005)], where a suitable regularization parameter is used to suppress the bias in the computed solution, by seeking a…”
Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems (2010, methodology): “E-mail: liucs@ntu.edu.tw 2 Center for Aerospace Research & Education, University of California, Irvine”