Square regularization matrices for large linear discrete ill‐posed problems

SUMMARY Large linear discrete ill‐posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large‐scale Tikhonov regularization problems. Copyright © 2012 John Wiley & Sons, Ltd.