Condition numbers of the mixed least squares-total least squares problem revisited

Unifying Least Squares, Total Least Squares and Data Least Squares

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

On the condition number of the total least squares problem

Condition Numbers for Structured Least Squares Problems

This paper studies the normwise perturbation theory for structured least squares problems. The structures under investigation are symmetric, persymmetric, skewsymmetric, Toeplitz and Hankel. We present the condition numbers for structured least squares. AMS subject classification (2000): 15A18, 65F20, 65F25, 65F50.

Generalizations of the total least squares problem

Recent advances in total least squares approaches for solving various errorsin-variables modeling problems are reviewed, with emphasis on the following generalizations: 1. the use of weighted norms as a measure of the data perturbation size, capturing prior knowledge about uncertainty in the data; 2. the addition of constraints on the perturbation to preserve the structure of the data matrix, m...

GLOBAL TOTAL LEAST SQUARES Global Total Least Squares

A method for the construction of open approximate models from vector time series Preface PhD research is a largely open proces in which a stimulating environment plays a crucial role. I am indebted to several people and institutions that shaped such an environment for me during the years since April 1990. First and for all, I would like to thank my supervisor, Christiaan Heij. He set me on the ...