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X2 Tests For The Choice Of The Regularization Parameter In Nonlinear Inverse Problems, J. L. Mead, C. C. Hammerquist
X2 Tests For The Choice Of The Regularization Parameter In Nonlinear Inverse Problems, J. L. Mead, C. C. Hammerquist
Jodi Mead
We address discrete nonlinear inverse problems with weighted least squares and Tikhonov regularization. Regularization is a way to add more information to the problem when it is ill-posed or ill-conditioned. However, it is still an open question as to how to weight this information. The discrepancy principle considers the residual norm to determine the regularization weight or parameter, while the χ2 method [J. Mead, J. Inverse Ill-Posed Probl., 16 (2008), pp. 175–194; J. Mead and R. A. Renaut, Inverse Problems, 25 (2009), 025002; J. Mead, Appl. Math. Comput., 219 (2013), pp. 5210–5223; R. A. Renaut, I. Hnetynkova, and J. L. …