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Keywords
(7)
Condition Number
Error Bound
Numerical Analysis
Partial Differential Equation
Singular Value
Singular Value Decomposition
Spectral Norm
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Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse
Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse,10.1007/s1054301002940,Bit Numerical Mathemati
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Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse
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Citations: 1
)
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Siegfried M. Rump
The
singular value decomposition
and
spectral norm
of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the
spectral norm
of a matrix are mandatory. We present various approaches to this together with some auxiliary useful estimates.
Journal:
Bit Numerical Mathematics  BIT
, vol. 51, no. 2, pp. 367384, 2011
DOI:
10.1007/s1054301002940
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References
(16)
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Journal:
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On Floating Point Errors in Cholesky
(
Citations: 18
)
James Demmel
Published in 1989.
Accuracy and stability of numerical algorithms (2. ed.)
(
Citations: 1299
)
Nicholas J. Higham
Published in 2002.
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(
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)
R. A. Horn
,
C. A. Johnson
Published in 1991.
A numerical approach to the proof of existence of solutions for elliptic problems
(
Citations: 36
)
Mitsuhiro T. Nakao
Journal:
Japan Journal of Industrial and Applied Mathematics  JPN J IND APPL MATH
, vol. 5, no. 2, pp. 313332, 1988
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(1)
An Elimination Method for Solving Bivariate Polynomial Systems: Eliminating the Usual Drawbacks
Eric Berberich
,
Pavel Emeliyanenko
,
Michael Sagraloff
Journal:
Computing Research Repository  CORR
, vol. abs/1010.1, 2010