English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we present explicit expressions for the mixed andcomponentwise condition numbers of the truncated total least squares (TTLS)solution of $A\boldsymbol{x} \approx \boldsymbol{b} $ under the genericitycondition, where $A$ is a $m\times n$ real data matrix and $\boldsymbol{b}$ isa real $m$-vector. Moreover, we reveal that normwise, componentwise and mixedcondition numbers for the TTLS problem can recover the previous correspondingcounterparts for the total least squares (TLS) problem when the truncated levelof for the TTLS problem is $n$. When $A$ is a structured matrix, the structuredperturbations for the structured truncated TLS (STTLS) problem are investigatedand the corresponding explicit expressions for the structured normwise,componentwise and mixed condition numbers for the STTLS problem are obtained.Furthermore, the relationships between the structured and unstructurednormwise, componentwise and mixed condition numbers for the STTLS problem arestudied. Based on small sample statistical condition estimation (SCE), reliablecondition estimation algorithms for both unstructured and structured normwise,mixed and componentwise are devised, which utilize the SVD of the augmentedmatrix $[A~\boldsymbol{b} ]$. The efficient proposed condition estimationalgorithms can be integrated into the SVD-based direct solver for the small andmedium size TTLS problem to give the error estimation for the numerical TTLSsolution. Numerical experiments are reported to illustrate the reliability ofthe proposed estimation algorithms, which coincide with our theoreticalresults.

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