Remarks on the root-clustering of a polynomial in a certain region in the complex plane
Authors:
E. I. Jury and S. M. Ahn
Journal:
Quart. Appl. Math. 32 (1974), 203-205
MSC:
Primary 12D10; Secondary 93B30
DOI:
https://doi.org/10.1090/qam/432611
MathSciNet review:
432611
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Abstract: A general formulation for the root clustering of a polynomial is given. An attempt has been made to answer an open question raised by Kalman.
- R. E. Kalman, Algebraic characterization of polynomials whose zeros lie in certain algebraic domains, Proc. Nat. Acad. Sci. U.S.A. 64 (1969), 818–823. MR 271132, DOI https://doi.org/10.1073/pnas.64.3.818
- E. I. Jury and S. M. Ahn, Symmetric and innerwise matrices for the root-clustering and root-distribution of a polynomial, J. Franklin Inst. 293 (1972), 433–450. MR 414840, DOI https://doi.org/10.1016/0016-0032%2872%2990056-7
- James Lucien Howland, Matrix equations and the separation of matrix eigenvalues, J. Math. Anal. Appl. 33 (1971), 683–691. MR 274470, DOI https://doi.org/10.1016/0022-247X%2871%2990088-6
- Peter Lancaster, Theory of matrices, Academic Press, New York-London, 1969. MR 0245579
- Richard D. Hill, Inertia theory for simultaneously triangulable complex matrices, Linear Algebra Appl. 2 (1969), 131–142. MR 245596, DOI https://doi.org/10.1016/0024-3795%2869%2990022-6
R. E. Kalman, Algebraic characterization of polynomials whose zeros lie in certain algebraic domains, Proc. Nat. Acad. Sci. 64, 818–823 (1969)
E. I. Jury and S. M. Ahn, Symmetric and innerwise matrices for the root-clustering and root-distribution of a polynomial, J. Franklin Inst. 293, 433–450. (1972)
J. L. Howland, Matrix equations and the separation of matrix eigenvalues, J. Math. Anal. Appl. 33, 683–691 (1971)
P. Lancaster, Theory of matrices, Academic Press, New York, 1969
R. D. Hill, Inertia theory for simultaneously triangulizable complex matrices, Linear Algebra and its Applications, 131–142 (1969)
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Article copyright:
© Copyright 1974
American Mathematical Society
