论文信息 - Sign test of multivariable real polynomials

Sign test of multivariable real polynomials

New theorems and procedures are presented for testing positivity and nonnegativity of a real polynomial in n real variables. The methods pertain to global as well as nonglobal or local sign tests for any closed intervals of the variables. A dimension growth is not required, and the methods depend on resolution of the solution of a set of n equations in n variables. Also provided is a simplified estimation of the computational effort involved in the present procedures, as compared to procedures where a dimension growth is required. Several illustrative examples are also provided.

Ezra Zeheb | E. Walach | E. Zeheb | E. Walach

[1] N. Bose,et al. On nonglobal positivity and domains of positivity of multivariable polynomials , 1977, Proceedings of the IEEE.

[2] Theodore A. Bickart,et al. Real polynomials: Nonnegativity and positivity , 1978 .

[3] J. Cruz,et al. The Parameter Variation Problem in State Feedback Control Systems , 1965 .

[4] N.K. Bose,et al. A multivariable polynomial nonnegativity test , 1976, Proceedings of the IEEE.

[5] N. Bose,et al. General procedure for multivariable polynomial positivity test with control applications , 1976 .

[6] Multivariate polynomial positivity test efficiency improvement , 1979, Proceedings of the IEEE.

[7] F. Wu. Existence of an operating point for a nonlinear circuit using the degree of mapping , 1974 .

[8] N. Bose,et al. Implementation of a new stability test for n-D filters , 1979 .

[9] N. Bose,et al. Tellegen's theorem and multivariable realizability theory† , 1974 .

[10] T. Kasami,et al. Positive Real Functions of Several Variables and Their Applications to Variable Networks , 1960 .

[11] E. Jury. Stability of multidimensional scalar and matrix polynomials , 1978, Proceedings of the IEEE.