Mixed, componentwise condition numbers and small sample statistical condition estimation for generalized spectral projections and matrix sign functions

Wei Guo Wang, Chern-Shuh Wang, Yi Min Wei, Peng Peng Xie

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The explicit expressions of mixed and componentwise condition numbers for the spectral projections, generalized spectral projections and sign functions for matrices and regular matrix pairs are derived. The condition numbers improve some known results of the normwise type and reveal the structured perturbations. Statistical condition estimation is applied to these problems which can be calculated efficiently.

Original languageEnglish
Pages (from-to)333-363
Number of pages31
JournalTaiwanese Journal of Mathematics
Volume20
Issue number2
DOIs
Publication statusPublished - 2016 Apr 1

Fingerprint

Mixed number
Matrix Sign Function
Generalized Projection
Spectral Projection
Condition number
Small Sample
Structured Perturbations

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{338baaa52e264d1aad23b97cf9612e49,
title = "Mixed, componentwise condition numbers and small sample statistical condition estimation for generalized spectral projections and matrix sign functions",
abstract = "The explicit expressions of mixed and componentwise condition numbers for the spectral projections, generalized spectral projections and sign functions for matrices and regular matrix pairs are derived. The condition numbers improve some known results of the normwise type and reveal the structured perturbations. Statistical condition estimation is applied to these problems which can be calculated efficiently.",
author = "Wang, {Wei Guo} and Chern-Shuh Wang and Wei, {Yi Min} and Xie, {Peng Peng}",
year = "2016",
month = "4",
day = "1",
doi = "10.11650/tjm.20.2016.5398",
language = "English",
volume = "20",
pages = "333--363",
journal = "Taiwanese Journal of Mathematics",
issn = "1027-5487",
publisher = "Mathematical Society of the Rep. of China",
number = "2",

}

Mixed, componentwise condition numbers and small sample statistical condition estimation for generalized spectral projections and matrix sign functions. / Wang, Wei Guo; Wang, Chern-Shuh; Wei, Yi Min; Xie, Peng Peng.

In: Taiwanese Journal of Mathematics, Vol. 20, No. 2, 01.04.2016, p. 333-363.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Mixed, componentwise condition numbers and small sample statistical condition estimation for generalized spectral projections and matrix sign functions

AU - Wang, Wei Guo

AU - Wang, Chern-Shuh

AU - Wei, Yi Min

AU - Xie, Peng Peng

PY - 2016/4/1

Y1 - 2016/4/1

N2 - The explicit expressions of mixed and componentwise condition numbers for the spectral projections, generalized spectral projections and sign functions for matrices and regular matrix pairs are derived. The condition numbers improve some known results of the normwise type and reveal the structured perturbations. Statistical condition estimation is applied to these problems which can be calculated efficiently.

AB - The explicit expressions of mixed and componentwise condition numbers for the spectral projections, generalized spectral projections and sign functions for matrices and regular matrix pairs are derived. The condition numbers improve some known results of the normwise type and reveal the structured perturbations. Statistical condition estimation is applied to these problems which can be calculated efficiently.

UR - http://www.scopus.com/inward/record.url?scp=84962016499&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962016499&partnerID=8YFLogxK

U2 - 10.11650/tjm.20.2016.5398

DO - 10.11650/tjm.20.2016.5398

M3 - Article

AN - SCOPUS:84962016499

VL - 20

SP - 333

EP - 363

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 2

ER -