Sufficient Conditions for Regularity and Singularity of Interval Matrices

Several verifiable sufficient conditions for regularity and singularity of interval matrices are given. As an application, a verifiable sufficient condition is derived for an interval matrix to have all eigenvalues real.

[1]  J. Rohn.  Checking positive definiteness or stability of symmetric interval matrices is NP-hard , 1994 .

[2]  Svatopluk Poljak,et al.  Checking robust nonsingularity is NP-hard , 1993, Math. Control. Signals Syst..

[3]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[4]  C. Jansson.  Calculation of exact bounds for the solution set of linear interval systems , 1997 .

[5]  A. Bartlett,et al.  On the eigenvalues of interval matrices , 1987, 26th IEEE Conference on Decision and Control.

[6]  Siegfried M. Rump.  Almost Sharp Bounds for the Componentwise Distance to the Nearest Singular Matrix , 1997 .

[7]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[8]  Arkadi Nemirovski,et al.  Several NP-hard problems arising in robust stability analysis , 1993, Math. Control. Signals Syst..

[9]  M. Mansour.  Robust stability of interval matrices , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[10]  J. Rohn.  Systems of linear interval equations , 1989 .

[11]  S. Rump.  Verification methods for dense and sparse systems of equations , 1994 .

[12]  Siegfried M. Rump,et al.  Bounds for the Componentwise Distance to the Nearest Singular Matrix , 1997, SIAM J. Matrix Anal. Appl..

[13]  J. Rohn.  Positive Definiteness and Stability of Interval Matrices , 1994, SIAM J. Matrix Anal. Appl..

[14]  A. Neumaier.  New techniques for the analysis of linear interval equations , 1984 .

[15]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[16]  Helmut Beeck,et al.  Zur Problematik der Hüllenbestimmung von Intervallgleichungssystemen , 1975, Interval Mathematics.

[17]  Willard L. Miranker,et al.  A new approach to scientific computation , 1983 .

[18]  E. Bareiss.  Sylvester’s identity and multistep integer-preserving Gaussian elimination , 1968 .

[19]  Siegfried M. Rump,et al.  Solving Algebraic Problems with High Accuracy , 1983, IMACS World Congress.

[20]  Jiri Rohn,et al.  Interval P-Matrices , 1996, SIAM J. Matrix Anal. Appl..

[21]  Arnold Neumaier,et al.  Linear Interval Equations , 1986, Interval Mathematics.

[22]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[23]  Jiri Rohn,et al.  A note on checking regularity of interval matrices , 1995 .

[24]  Christian Jansson,et al.  An Algorithm for Checking Regularity of Interval Matrices , 1999, SIAM J. Matrix Anal. Appl..

[25]  W. Prager,et al.  Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides , 1964 .