Results 271 to 280 of about 16,280 (299)

On the Inversion of Ill-Conditioned Matrices

IEEE Transactions on Reliability, 1980
A recent paper presented a modification of the Gauss-Jordan method for inverting a matrix which avoids loss of accuracy due to a type of ill-conditioning which leads to subtractive cancellation. This paper shows the relationship between the standard and modified techniques, and why and when the latter is effective.
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Conditions for Boundedness of Hankel Matrices

Bulletin of the London Mathematical Society, 1994
The author obtains a new sufficient condition for an infinite Hankel matrix \((a_{i+ j})_{i, j\geq 0}\) to determine a bounded linear operator on a Hilbert space. One form of this condition is that we can write \(a_ k= \lambda_ k \alpha_ k\), with \(\{\lambda_ k\}\) a decreasing sequence in \(\ell^ 2\) and \(\{\alpha_ k\}\) satisfying, for some ...
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A consideration on the condition number of extremely ill-conditioned matrices

2013 European Conference on Circuit Theory and Design (ECCTD), 2013
As for a matrix A we examine two problems: (a) To find the upper and the lower bound of Cond2(A) in terms of two coefficients p1 and pn-1 (see Section 2) of the characteristic polynomial of AA T, and (b) proof of existence of a matrix A having considerably larger condition number than that obtained in the previous papers. The connection between (a) and
Tetsuo Nishi, Siegfried M. Rump, Shin'ichi Oishi   +2 more
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Nonnormality and Jordan Condition Numbers of Matrices

Journal of the ACM, 1969
A lower bound for the departure from normality of an n X n matrix A is given. Furthermore, various inequalities are obtained for certain condition numbers associated with the reduction of A to its Jordan canonical form.
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On sufficient conditions for the stability of Interval matrices

Journal of the Franklin Institute, 1989
New sufficient conditions are developed for the stability analysis of an interval matrix [B,C]. The approach presented uses similarity transformations diagonalizing a matrix \(A\in [B,C]\) and an estimate of the norm of the error matrix. Numerical examples are given.
Chou, Jyh-Horng, Horng, Ing-Rong
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A Six-Point Condition for Ordinal Matrices

Journal of Computational Biology, 1997
Ordinal assertions in an evolutionary context are of the form "species s is more similar to species x than the species y" and can be deduced from a distance matrix M of interspecies dissimilarities (M[s, x] < M[s, y]). Given species x and y, the ordinal binary character cxy of M is defined by cxy(s) = 1 if and only if M[s,x] < M[s, y], for all species ...
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Condition Number Estimation for Sparse Matrices

SIAM Journal on Scientific and Statistical Computing, 1981
The LINPACK package of linear equation solving software provides a reliable and inexpensive algorithm for estimating the condition number of a dense matrix. The direct generalization to banded or sparse matrices is reliable, but not necessarily inexpensive.
Grimes, Roger G., Lewis, John G.
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Matrices, Norms and Conditioning

2014
To measure the size of vector and matrices we use norms. In this chapter, we introduce and study three vector norms and define and use the corresponding matrix norms. One of the goals is to estimate a bound on the error in the solution \(\boldsymbol{x}\) of a linear system \(\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}\) when there exists an ...
Tom Lyche, Jean-Louis Merrien
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Condition numbers for various FEM matrices

IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010), 1999
Summary: A detailed study is presented that examines the inter-relationships between condition numbers of finite element method (FEM) matrices based on various interpolatory and hierarchical tangential vector finite elements (TVFEs). The validity of the generally accepted postulate that interpolatory higher order TVFEs lead to better conditioned ...
Andersen, L. S., Volakis, J. L.
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A note on conditioning, stability and collocation matrices

Applied Mathematics and Computation, 1989
The authors discuss the well-conditioning of boundary value problems, pointing out that the concept is not always a direct analogue of the well-conditioning of matrices. The condition number of numerical schemes, using discretizations of the differential operator, is examined.
Uri M. Ascher, Georg Bader
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