Applications of the householder transformation to Ridge-type estimation methods

摘要

Ridge-type estimation methods, used as a means to overcome the effects of ill-conditioning in nonlinear inverse problems, have recently been modified to include the use of observation statistics in the solution process and to compute a different biasing parameter for each model variable. These ridge-type estimation methods have commonly been implemented using Cholesky decomposition techniques in lieu of standard matrix inversion. However, in many applications it is desirable touse more advanced Householder transformation methods in the solution process for enhanced computational efficiency and numerical stability. In this presentation, modifications of the Householder orthogonal transformation have been made in order to efficiently accomodate ridge-type estimation methods. Results have been verified and are provided in algorithmic form.