Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

Motivated by the recently popular probabilistic methods for low‐rank approximations and
randomized algorithms for the least squares problems, we develop randomized algorithms …

Condition number plays an important role in perturbation analysis, the latter is a tool to judge
whether a numerical solution makes sense, especially for ill-posed problems. In this paper …

We present the Kronecker-product-based formulae for the normwise, mixed, and
componentwise condition numbers of the multidimensional total least squares (TLS) …

In this paper, under the genericity condition, we study the condition estimation of the total
least squares (TLS) problem based on small sample condition estimation (SCE), which can …

In this note, we present perturbation analysis for the total least squares (Tls) problems under
the genericity condition. We review the three condition numbers proposed respectively by …

We present an explicit expression for the condition number of the truncated total least
squares (TLS) solution of Ax≈b. This expression is obtained using the notion of the Fréchet …

This paper is devoted to perturbation analysis of the total least squares problem with linear
equality constraint (TLSE). Different magnitudes of perturbations in input data are taken into …

In many linear parameter estimation problems, one can use the mixed least squares–total
least squares (MTLS) approach to solve them. This paper is devoted to the perturbation …

Many recent data analysis models are mathematically characterized by a multidimensional
total least squares problem with linear equality constraints (TLSE). In this paper, an explicit …