Arnoldi–Tikhonov regularization methods

✍ Scribed by Bryan Lewis; Lothar Reichel

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 814 KB
• Volume: 226
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.05.003

✦ Synopsis

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.