TY - EJOU AU - Liu, Chein-Shan AU - Kuo, Chung-Lun TI - A Dynamical Tikhonov Regularization Method for Solving Nonlinear Ill-Posed Problems T2 - Computer Modeling in Engineering \& Sciences PY - 2011 VL - 76 IS - 2 SN - 1526-1506 AB - 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 of nonlinear ill-posed systems under noise are examined, revealing that the present OVDA has a good computational efficiency and accuracy. KW - Ill-posed systems KW - Tikhonov regularization KW - Dynamical Tikhonov regularization KW - Optimal vector driven algorithm (OVDA) KW - Landweber-Scherzer iterative algorithm DO - 10.3970/cmes.2011.076.109