On the condition number of the total least squares problem with linear equality constraint

08/19/2020
by   Qiaohua Liu, et al.
0

This paper is devoted to the condition number of the total least squares problem with linear equality constraint (TLSE). With novel techniques, closed formulae for the normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Compact expressions and upper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. Explicit condition number expressions and perturbation bound for the TLS problem can be recovered from our estimates. For random TLSE problems, numerical experiments illustrate the sharpness of the estimates based on normwise condition numbers, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/17/2020

A contribution to condition numbers of the multidimensional total least squares problem with linear equality constraint

This paper is devoted to condition numbers of the multidimensional total...
12/03/2020

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

A new closed formula for the first order perturbation estimate of the mi...
04/25/2020

Condition numbers for the truncated total least squares problem and their estimations

In this paper, we present explicit expressions for the mixed and compone...
05/30/2019

On condition numbers of symmetric and nonsymmetric domain decomposition methods

Using oblique projections and angles between subspaces we write conditio...
10/12/2019

Structured condition number for multiple right-hand side linear systems with parameterized quasiseparable coefficient matrix

In this paper, we consider the structured perturbation analysis for mult...
02/15/2022

On the entropy numbers and the Kolmogorov widths

Direct estimates between linear or nonlinear Kolmogorov widths and entro...