• REGULARIZATION OF ILL-CONDITIONED LINEAR SYSTEMS

Joseph Acquah, Ernest Danso-Addo

Abstract


In this paper, we examined various regularization methods for obtaining meaningfully approximations to ill-conditioned linear systems. The methods considered include; Preconditioning, Truncated Singular Value Decomposition (T.S.V.D) and Tikhonov Regularization. These methods were applied to obtain stable solution estimates for the Hilbert system, Boundary Value Problems (B.V.P) and Discretized Fredholm Integral Equation of the First Kind. Also, different methods for choosing an optimal regularization parameter including the L-Curve method were considered.


Keywords


Ill-Conditioned, Preconditioning, Truncated Singular Value Decomposition, Tikhonov Regularization and L-Curve.

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