Explicit SOS decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov lemma

2007 ◽  
Author(s):  
Erin M. Aylward ◽  
Sleiman M. Itani ◽  
Pablo A. Parrilo
Keyword(s):  
Polynomial Matrices ◽  
Univariate Polynomial

Interpolation algorithm of Leverrier–Faddev type for polynomial matrices

2006 ◽  
Vol 42 (3-4) ◽  
pp. 345-361 ◽  
Author(s):  
Marko D. Petković ◽  
Predrag S. Stanimirović
Keyword(s):  
Interpolation Algorithm ◽  
Polynomial Matrices

scholarly journals Differential resolvents of minimal order and weight

2004 ◽  
Vol 2004 (54) ◽  
pp. 2867-2893
Author(s):  
John Michael Nahay
Keyword(s):  
Upper Bound ◽  
Minimal Order ◽  
Determinantal Formula ◽  
Differential Field ◽  
Nonzero Coefficient ◽  
Univariate Polynomial ◽  
Linear Differential ◽  
Indicial Equation

We will determine the number of powers ofαthat appear with nonzero coefficient in anα-power linear differential resolvent of smallest possible order of a univariate polynomialP(t)whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of anα-resolvent of smallest possible weight. We will then compute the indicial equation, apparent singularities, and Wronskian of the Cockleα-resolvent of a trinomial and finish with a related determinantal formula.

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