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Some New Bounds on the Condition Numbers of Optimally Scaled Matrices

Authors:

T. I. Fenner,

G. LoizouAuthors Info & Claims

Journal of the ACM (JACM), Volume 21, Issue 3

Pages 514 - 524

https://doi.org/10.1145/321832.321849

Published: 01 July 1974 Publication History

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Abstract

New lower bounds on the minimal condition numbers of a matrix with respect to both one-sided and two-sided scaling by diagonal matrices are obtained. These bounds improve certain results obtained by F. L. Bauer.

References

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Cited By

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Traina DMacchiarella GSarkar T(2007)New general formulation of the Cauchy method for the accurate model extraction of higher order microwave systemsMicrowave and Optical Technology Letters10.1002/mop.2262749:8(1957-1961)Online publication date: 29-May-2007
https://doi.org/10.1002/mop.22627
(1997)Optimally scalable matricesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences10.1098/rsta.1977.0147287:1345(307-349)Online publication date: Jan-1997
https://doi.org/10.1098/rsta.1977.0147
Nett CManousiouthakis V(1987)Euclidean condition and block relative gain: Connections, conjectures, and clarificationsIEEE Transactions on Automatic Control10.1109/TAC.1987.110461832:5(405-407)Online publication date: May-1987
https://doi.org/10.1109/TAC.1987.1104618
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Index Terms

Some New Bounds on the Condition Numbers of Optimally Scaled Matrices
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
2. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Pre- and post-conditions

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Published In

Journal of the ACM Volume 21, Issue 3

July 1974

173 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321832

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1974

Published in JACM Volume 21, Issue 3

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Traina DMacchiarella GSarkar T(2007)New general formulation of the Cauchy method for the accurate model extraction of higher order microwave systemsMicrowave and Optical Technology Letters10.1002/mop.2262749:8(1957-1961)Online publication date: 29-May-2007
https://doi.org/10.1002/mop.22627
(1997)Optimally scalable matricesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences10.1098/rsta.1977.0147287:1345(307-349)Online publication date: Jan-1997
https://doi.org/10.1098/rsta.1977.0147
Nett CManousiouthakis V(1987)Euclidean condition and block relative gain: Connections, conjectures, and clarificationsIEEE Transactions on Automatic Control10.1109/TAC.1987.110461832:5(405-407)Online publication date: May-1987
https://doi.org/10.1109/TAC.1987.1104618
Faddeev DFaddeeva V(1981)Computational methods of linear algebraJournal of Soviet Mathematics10.1007/BF0108654415:5(531-650)Online publication date: 1981
https://doi.org/10.1007/BF01086544

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Eigenvalue condition numbers and pseudospectra of Fiedler matrices

Optimally scaled and optimally conditioned Vandermonde and Vandermonde-like matrices

Condition Numbers of Random Triangular Matrices

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