Open AccessOn Stability of Parametrized Families of Polynomials and Matrices
Author(s) -
Handan Akyar,
Taner Büyükköroğlu,
Vakıf Dzhafarov
Publication year - 2010
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2010/687951
Subject(s) - mathematics , multilinear map , schur's theorem , stability (learning theory) , hurwitz matrix , polynomial , polynomial matrix , parametric statistics , matrix (chemical analysis) , schur polynomial , hurwitz polynomial , set (abstract data type) , multilinear algebra , schur product theorem , combinatorics , pure mathematics , matrix polynomial , algebra over a field , schur complement , schur decomposition , classical orthogonal polynomials , orthogonal polynomials , mathematical analysis , wilson polynomials , gegenbauer polynomials , eigenvalues and eigenvectors , division algebra , quantum mechanics , physics , materials science , computer science , composite material , machine learning , filtered algebra , programming language , statistics
The Schur and Hurwitz stability problems for a parametric polynomialfamily as well as the Schur stability problem for a compact set of realmatrix family are considered. It is established that the Schur stabilityof a family of real matrices is equivalent to the nonsingularityof the family {2−2+∶∈,∈[−1,1]} if has atleast one stable member. Based on the Bernstein expansion of amultivariable polynomial and extremal properties of a multilinearfunction, fast algorithms are suggested
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