Arnoldi-Tikhonov regularization methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:226

Article; Proceedings Paper

Lewis, Bryan²  Reichel, Lothar¹ 

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Rocketcalc LLC, Kent, OH 44240 USA

关键词: Ill-posed problem;    Inverse problem;    Regularization;    Arnoldi decomposition;    Discrepancy principle;   

DOI  :  10.1016/j.cam.2008.05.003

来源: Elsevier

【 摘 要 】

Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix. Computed examples illustrate that this approach may require fewer matrix-vector product evaluations and, therefore, less arithmetic work. Moreover, the proposed range-restricted Arnoldi-Tikhonov regularization method does not require the adjoint matrix and, hence, is convenient to use for problems for which the adjoint is difficult to evaluate. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free