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Ngo, C., Yashtini, M. and Zhang, H.C. (2015) An Alternating Direction Approximate Newton Algorithm for Ill-Conditioned Inverse Problems with Application to Parallel MRI. Journal of the Operations Research Society of China, 3, 139-162.
http://dx.doi.org/10.1007/s40305-015-0078-y

has been cited by the following article:

• TITLE: A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions

  AUTHORS: Anastasia-Dimitra Lipitakis

  KEYWORDS: Adaptive Algorithms, Algorithmic Modelling, Approximate Inverse, Incomplete LU Factorization, Approximate Decomposition, Unsymmetric Linear Systems, Preconditioned Iterative Methods, Systems of Irregular Structure

  JOURNAL NAME: Applied Mathematics, Vol.7 No.11, July 12, 2016

  ABSTRACT: A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.