# The truncated*SVD* as a method for regularization

Part II Numerical Mathematics

- Received:
- Revised:

DOI: 10.1007/BF01937276

- Cite this article as:
- Hansen, P.C. BIT (1987) 27: 534. doi:10.1007/BF01937276

- 220 Citations
- 1.2k Downloads

## Abstract

The truncated singular value decomposition (SVD) is considered as a method for regularization of ill-posed linear least squares problems. In particular, the truncated SVD solution is compared with the usual regularized solution. Necessary conditions are defined in which the two methods will yield similar results. This investigation suggests the truncated SVD as a favorable alternative to standard-form regularization in cases of ill-conditioned matrices with well-determined numerical rank.

### AMS subject classification

65F2065F30### Keywords

truncated SVDregularization in standard formperturbation theory for truncated SVDnumerical rank## Copyright information

© BIT Foundations 1987