Skip to main content

New Insights into the RLS Algorithm


The recursive least squares (RLS) algorithm is one of the most popular adaptive algorithms that can be found in the literature, due to the fact that it is easily and exactly derived from the normal equations. In this paper, we give another interpretation of the RLS algorithm and show the importance of linear interpolation error energies in the RLS structure. We also give a very efficient way to recursively estimate the condition number of the input signal covariance matrix thanks to fast versions of the RLS algorithm. Finally, we quantify the misalignment of the RLS algorithm with respect to the condition number.

Author information



Corresponding author

Correspondence to Jacob Benesty.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Benesty, J., Gänsler, T. New Insights into the RLS Algorithm. EURASIP J. Adv. Signal Process. 2004, 243857 (2004).

Download citation

Keywords and phrases

  • adaptive algorithms
  • normal equations
  • RLS
  • fast RLS
  • condition number
  • linear interpolation