Differentiation of Operator Functions and Perturbation Bounds

Rajendra Bhatia; Dinesh Singh; Kalyan B. Sinha

doi:10.1007/s002200050279

Differentiation of Operator Functions and Perturbation Bounds

Communications in Mathematical Physics ◽

10.1007/s002200050279 ◽

1998 ◽

Vol 191 (3) ◽

pp. 603-611 ◽

Cited By ~ 8

Author(s):

Rajendra Bhatia ◽

Dinesh Singh ◽

Kalyan B. Sinha

Keyword(s):

Perturbation Bounds ◽

Operator Functions

Perturbation bounds for certain operator functions

Mathematical Inequalities & Applications ◽

10.7153/mia-04-53 ◽

2001 ◽

pp. 609-617

Author(s):

Jaspal Singh Aujla

Keyword(s):

Perturbation Bounds ◽

Operator Functions

Characteristic operator functions for quantum input-plant-output models and coherent control

Journal of Mathematical Physics ◽

10.1063/1.4906136 ◽

2015 ◽

Vol 56 (1) ◽

pp. 013506 ◽

Cited By ~ 1

Author(s):

John E. Gough

Keyword(s):

Coherent Control ◽

Characteristic Operator ◽

Operator Functions

Applications of Paz's inequality to perturbation bounds for Markov chains

Linear Algebra and its Applications ◽

10.1016/s0024-3795(97)00042-6 ◽

1998 ◽

Vol 268 ◽

pp. 183-196 ◽

Cited By ~ 23

Author(s):

Stephen J. Kirkland ◽

Michael Neumann ◽

Bryan L. Shader

Keyword(s):

Markov Chains ◽

Perturbation Bounds

Approximation theorems for cosine operator functions

Acta Mathematica Academiae Scientiarum Hungaricae ◽

10.1007/bf01896469 ◽

1977 ◽

Vol 29 (1-2) ◽

pp. 69-76 ◽

Cited By ~ 8

Author(s):

B. Nagy

Keyword(s):

Approximation Theorems ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions

Multiplicative perturbation bounds for multivariate multiple linear regression in Schatten p-norms

Linear Algebra and its Applications ◽

10.1016/j.laa.2021.03.039 ◽

2021 ◽

Author(s):

Jocelyn T. Chi ◽

Ilse C.F. Ipsen

Keyword(s):

Linear Regression ◽

Multiple Linear Regression ◽

Perturbation Bounds ◽

Multiplicative Perturbation

Perturbation Bounds and Condition Numbers for a Complex Indefinite Linear Algebraic System

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.201015.140316a ◽

2016 ◽

Vol 6 (2) ◽

pp. 211-221 ◽

Cited By ~ 1

Author(s):

Lei Zhu ◽

Wei-Wei Xu ◽

Xing-Dong Yang

Keyword(s):

Algebraic System ◽

Condition Numbers ◽

Linear Algebraic System ◽

Science And Engineering ◽

Numerical Examples ◽

Interest In Science ◽

Perturbation Bounds

AbstractWe consider perturbation bounds and condition numbers for a complex indefinite linear algebraic system, which is of interest in science and engineering. Some existing results are improved, and illustrative numerical examples are provided.

Linearization of operator functions on arbitrary open sets

Integral Equations and Operator Theory ◽

10.1007/bf01682738 ◽

1978 ◽

Vol 1 (1) ◽

pp. 19-27 ◽

Cited By ~ 8

Author(s):

Bert den Boer

Keyword(s):

Operator Functions

Rigorous Perturbation Bounds of Some Matrix Factorizations

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/090778535 ◽

2010 ◽

Vol 31 (5) ◽

pp. 2841-2859 ◽

Cited By ~ 16

Author(s):

X.-W. Chang ◽

D. Stehlé

Keyword(s):

Matrix Factorizations ◽

Perturbation Bounds

Perturbation Bounds for Determinants and Characteristic Polynomials

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/070704770 ◽

2008 ◽

Vol 30 (2) ◽

pp. 762-776 ◽

Cited By ~ 30

Author(s):

Ilse C. F. Ipsen ◽

Rizwana Rehman

Keyword(s):

Characteristic Polynomials ◽

Perturbation Bounds

On perturbation bounds for continuous-time Markov chains

Statistics & Probability Letters ◽

10.1016/j.spl.2014.01.031 ◽

2014 ◽

Vol 88 ◽

pp. 66-72 ◽

Cited By ~ 20

Author(s):

A.I. Zeifman ◽

V.Yu. Korolev

Keyword(s):

Markov Chains ◽

Continuous Time ◽

Perturbation Bounds ◽

Continuous Time Markov Chains