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On Schur \(D\)-stable matrices.(English)Zbl 0933.15035

Summary: It is shown that vertex stability implies Schur \(D\)-stability for real \(2\times 2\) matrices and real \(n\times n\) tridiagonal matrices. Additional results describing the class of \(n\times n\) complex Schur \(D\)-stable matrices are given.

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors

Cite

References:

[1]Bhaya, A.; Kaszkurewicz, E., On discrete-time diagonal and \(D\)-stability, Linear Alg. Appl., 187, 87-104 (1993) ·Zbl 0780.15010
[2]Cross, G. W., Three types of matrix stability, Linear Alg. Appl., 20, 253-263 (1978) ·Zbl 0376.15007
[3]Golub, Gene H., Charles Van Loan, Matrix Computations (1983), John Hopkins University Press: John Hopkins University Press Baltimore, MD ·Zbl 0559.65011
[4]Halmos, P., A Hilbert Space Problem Book (1982), Springer: Springer New York ·Zbl 0202.12801
[5]Hershkowitz, D., Recent directions in matrix stability, Linear Alg. Appl., 171, 161-186 (1992) ·Zbl 0759.15010
[6]Horn, Roger A.; Johnson, Charles R., Matrix Analysis (1993), Cambridge University Press: Cambridge University Press Cambridge ·Zbl 0704.15002
[7]Johnson, C. R.; Nylen, P., Monotonicity properties of norms, Linear Alg. Appl., 148, 43-58 (1991) ·Zbl 0717.15015
[8]Marden, M., Geometry of the Zeros of a Polynomial in a Complex Variable, Math Surveys III (1949), American Mathematical Society: American Mathematical Society Providence, RI ·Zbl 0038.15303
[9]Mills, W. L.; Mullis, C. T.; Roberts, R. A., Digital filter realizations without overflow oscillations, IEEE Trans. Acoustics Speech Signal Process, ASSP-26, 4, 334-338 (1978) ·Zbl 0415.93040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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