A direct method for a regularized least-squares problem

2009 ◽  
Vol 16 (8) ◽  
pp. 649-675 ◽  
Author(s):  
Tommy Elfving ◽  
Ingegerd Skoglund
Keyword(s):  
Least Squares ◽  
Direct Method ◽  
Least Squares Problem ◽  
Regularized Least Squares ◽  
A Direct Method

Linear Least-Squares Computations Using Givens Transformations

1983 ◽  
Vol 37 (4) ◽  
pp. 225-233 ◽  
Author(s):  
J. A. R. Blais
Keyword(s):  
Least Squares ◽  
Error Estimates ◽  
Data Storage ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Direct Method ◽  
Linear Least Squares ◽  
Normal Equations ◽  
Estimation Problems ◽  
A Direct Method

Givens transformations provide a direct method for solving linear least-squares estimation problems without forming the normal equations. This approach has been shown to be particularly advantageous in recursive situations because of characteristics related to data storage requirements, numerical stability and computational efficiency. The following discussion will concentrate on the problem of updating least-squares parameter and error estimates using Givens transformations. Special attention will be given to photogrammetric and geodetic applications.

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