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Journal of Optimization Theory and Applications

, Volume 83, Issue 1, pp 217–222 | Cite as

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

  • S. George
  • M. T. Nair
Technical Note

Abstract

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution\(\hat x\) belongs to the range of the operator (T*T) v , o<v≤1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2≤v≤1.

Key Words

Ill-posed operator equations Tikhonov regularization minimal-norm least-squares solution parameter choice strategy discrepancy principle Morozov's method Arcangeli's method optimal rate 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • S. George
    • 1
  • M. T. Nair
    • 1
  1. 1.Department of MathematicsGoa UniversityGoaIndia

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