Chein-Shan Liu1, Chung-Lun Kuo2
CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 109-132, 2011, DOI:10.3970/cmes.2011.076.109
Abstract The Tikhonov method is a famous technique for regularizing ill-posed systems. In this theory a regularization parameter α needs to be determined. Based-on an invariant-manifold defined in the space of (x,t) and from the Tikhonov minimization functional, we can derive an optimal vector driven system of nonlinear ordinary differential equations (ODEs). In the Optimal Vector Driven Algorithm (OVDA), the optimal regularization parameter αk is presented in the iterative solution of x, which means that a dynamical Tikhonov regularization method is involved in the solution of nonlinear ill-posed problem. The OVDA is an extension of the Landweber-Scherzer iterative algorithm. Numerical examples… More >
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