Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations. (Q2889380)

This paper explores some intrinsic characteristics of accuracy and stability for the truncated singular value decomposition (TSVD) and the Tikhonov regularization (TR). Both regularization techniques are applied to numerical solutions of partial differential equations (PDE).NEWLINENEWLINEThe authors derive new bounds for the contition number and the effective condition number, which is used to improve conditioning by TSVD and TR. A brief error analysis is done and error bounds are derived. The obtained results are illustrated by numerical experiments with the discrete Laplace equation.