Total Least Squares

A note on the scaled total least squares problem

In this note, we present two results on the scaled total least squares problem. First, we discuss the relation between the scaled total least squares and the least squares problems. We derive an upper bound for the difference between the scaled total least squares solution and the least squares solution and establish a quantitative relation between the scaled total least squares residual and th...

Bibliography on total least squares and related methods

The class of total least squares methods has been growing since the basic total least squares method was proposed by Golub and Van Loan in the 70’s. Efficient and robust computational algorithms were developed and properties of the resulting estimators were established in the errors-in-variables setting. At the same time the developed methods were applied in diverse areas, leading to broad lite...

An Introduction to Total Least Squares

Systolic Algorithms for Recursive Total Least Squares Parameter Estimation and Mixed RLS/RTLS Problems

Total least squares parameter estimation is an alternative to least squares estimation though much less used in practice, partly due to the absence of eecient recursive algorithms or parallel architectures. Here it is shown how previously developed systolic algorithms/architectures for recursive least squares estimation can be used for recursive total least squares problems. Unconstrained as we...

Total Least Squares Approach to Modeling: A Matlab Toolbox

This paper deals with a mathematical method known as total least squares or orthogonal regression or error-in-variables method. The mentioned method can be used for modeling of static and also dynamic processes. A wide area of other applications is in signal and image processing. We also present a Matlab toolbox which can solve basic problems related to the total least squares method in the mod...

Simultaneous Spectrophotometric Determination of Iron, Cobalt and Copper by Partial Least-Squares Calibration Method in Micellar Medium

Iron, cobalt and copper are metals, which appear together in many real samples, both natural and artificial. Recently a classical univariate micellar colorimetric method has been developed for determination of these metal ions. The organized molecular assemblies such as micelles are used in spectroscopic measurements due to their possible effects on the systems of interest. The ability of mi...