QR Factorization of the Jacobian in Some Structured Nonlinear Least Squares Problems

Åke Björck ()
Additional contact information
Åke Björck: Linköping University, Department of Mathematics

A chapter in Total Least Squares and Errors-in-Variables Modeling, 2002, pp 225-234 from Springer

Abstract: Abstract For solving nonlinear least squares problems a Gauss—Newton trust region method is often employed. In the case of orthogonal distance regression it has been believed that solving the resulting linear problem at each trust region step by computing the QR factorization of the full Jacobian matrix would be very inefficient. By taking full advantage of the structure of the sparse blocks in the QR factorization of the Jacobian, we derive here an algorithm with the same overall complexity, which uses a QR factorization of the full Jacobian matrix. The same observation applies also to sparse structured total least squares problems, where similarly structured Jacobian matrices occur.

Keywords: orthogonal distance regression; nonlinear errors-in-variables; structured total least squares; nonlinear least squares. (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-3552-0_20

Ordering information: This item can be ordered from
http://www.springer.com/9789401735520

DOI: 10.1007/978-94-017-3552-0_20

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().