Probabilistic Estimation of Matrix Condition Number

被引：0

作者：

Antyufeev V.S. ^{[1
,2
]}

机构：

[1] Institute Numerical Mathematics and Mathematical Geophysics SB RAS, 6, Akad. Lavrent’eva pr, Novosibirsk

[2] Novosibirsk State University, 1, Pirogova St, Novosibirsk

来源：

Journal of Mathematical Sciences | 2020年 / 246卷 / 6期

关键词：

D O I：

10.1007/s10958-020-04778-1

中图分类号：

学科分类号：

摘要：

We consider ill-conditioned matrices of systems of linear algebraic equations with random error of vector right-hand side. We study the condition number ν of the matrix of the system. We show that, under certain natural assumptions, the number ν can be considerably diminished. Bibliography: 3 titles. Illustrations: 3 figures. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：755 / 762

页数：7

共 50 条

[1] PROBABILISTIC BOUNDS FOR THE MATRIX CONDITION NUMBER WITH EXTENDED LANCZOS BIDIAGONALIZATION
Gaaf, Sarah W.
Hochstenbach, Michiel E.
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2015, 37 (05): : S581 - S601
[2] Taylor's theorem for matrix functions with applications to condition number estimation
Deadman, Edvin
Relton, Samuel D.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 504 : 354 - 371
[3] Estimation of a Structured Covariance Matrix with a Condition Number Constraint for Radar Applications
Pallotta, L.
Aubry, A.
De Maio, A.
Farina, A.
[J]. 2012 IEEE RADAR CONFERENCE (RADAR), 2012,
[4] COMPUTING THE FRECHET DERIVATIVE OF THE MATRIX EXPONENTIAL, WITH AN APPLICATION TO CONDITION NUMBER ESTIMATION
Al-Mohy, Awad H.
Higham, Nicholas J.
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (04) : 1639 - 1657
[5] Maximum Likelihood Estimation of a Structured Covariance Matrix With a Condition Number Constraint
Aubry, Augusto
De Maio, Antonio
Pallotta, Luca
Farina, Alfonso
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2012, 60 (06) : 3004 - 3021
[6] Probabilistic Analysis of the Grassmann Condition Number
Amelunxen, Dennis
Buergisser, Peter
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2015, 15 (01) : 3 - 51
[7] Probabilistic Analysis of the Grassmann Condition Number
Dennis Amelunxen
Peter Bürgisser
[J]. Foundations of Computational Mathematics, 2015, 15 : 3 - 51
[8] ESTIMATE FOR THE CONDITION NUMBER OF A MATRIX
CLINE, AK
MOLER, CB
STEWART, GW
WILKINSON, JH
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (02) : 368 - 375
[9] BOUNDS ON CONDITION NUMBER OF MATRIX
黄鸿慈
[J]. Science Bulletin, 1981, (07) : 668 - 668
[10] On the condition number of a Kreiss matrix
Charpentier, Stephane
Fouchet, Karine
Zarouf, Rachid
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2023, 66 (04): : 1376 - 1390

← 1 2 3 4 5 →