Polynomial Definiteness and Semidefiniteness

[+] Author and Article Information
Chiou-Shiun Chen

Department of Electrical Engineering, Akron University, Akron, Ohio

Edwin Kinnen

Department of Electrical Engineering, University of Rochester, Rochester, N. Y.

J. Basic Eng 92(2), 394-397 (Jun 01, 1970) (4 pages) doi:10.1115/1.3425007 History: Received December 23, 1969; Online October 27, 2010


A reduction procedure is described for determining the sign definiteness and semidefiniteness of an mth order, n dimensional real polynomial. The higher order polynomial is reduced to a quadratic form in new variables such that conditions can be obtained on the coefficients of the individual terms of the original polynomial. The procedure presents sufficient conditions only. It has been found, however, to be a relatively systematic technique for engineering stability problems where alternate effective methods for determining sign definiteness are unknown.

Copyright © 1970 by ASME
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