Fraction-free computation of the unit-circle resultant with any singularity profile

References

• Bézout É. Recherchez sur le degré des équations résultantes de l‘évanouissement des inconnues et sur le moyens qu'il convient d'employer pour trouver ces équations. Mem Acad Paris. 1764;288:338.
   Google Scholar
• Zippel R. Effective polynomial computation. Ithaca (NY): Cornell University; 1994.
   Google Scholar
• Sylvester J. On a theory of Syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm functions, and that of the greatest Algebraical common measure. Phil Trans Roy Soc London. 1853;143:407–548. doi: 10.1098/rstl.1853.0018
   Google Scholar
• Collins GE. Subresultants and reduced polynomial remainder sequences. J Assoc Comp Mach. 1967;14(1):128–142. doi: 10.1145/321371.321381
   Web of Science ®Google Scholar
• Brown WS. On Euclid's algorithm and the computation of polynomial greatest common divisors. J Assoc Comp Mach. 1971;18(4):478–504. doi: 10.1145/321662.321664
   Web of Science ®Google Scholar
• Brown WS, Traub JF. On Euclid's algorithm and the theory of subresultants. J Assoc Comp Mach. 1971;18(4):505–514. doi: 10.1145/321662.321665
   Web of Science ®Google Scholar
• Basu S, Pollack R, Roy MF. Algorithms in real algebraic geometry. 2nd ed. Berlin: Springer-Verlag; 2008.
   Google Scholar
• Lev-Ari H, Bistritz Y, Kailath T. Generalized Bezoutians and families of efficient zero-location procedures. IEEE Trans Circ Syst. 1991;38:170–186. doi: 10.1109/31.68295
   Google Scholar
• Lifshitz A, Bistritz Y. A fraction-free unit-circle zero location test for a polynomial with any singularity profile. Linear Multilinear Algebra. 2019;67(7):1420–1459. doi:10.1080/03081087.2018.1455802
   Web of Science ®Google Scholar
• Lancaster P, Tismenetsky M. The theory of matrices, 2nd edition with applications. Cambridge (MA): Academic Press; 1985.
   Google Scholar
• Bistritz Y. Zero location of polynomials with respect to the unit-circle unhampered by nonessential singularities. IEEE Trans Circ Syst I Fundam Theory Appl. 2002;49(3):305–314. doi: 10.1109/81.989164
   Google Scholar
• Bistritz Y. Zero location with respect to the unit-circle of discrete-time linear system polynomials. Proc IEEE. 1984;72(9):1131–1142. doi: 10.1109/PROC.1984.12993
   Web of Science ®Google Scholar
• Bistritz Y. A circular stability test for general polynomials. Syst Control Lett. 1986;7(2):89–97. doi: 10.1016/0167-6911(86)90013-7
   Web of Science ®Google Scholar
• Bistritz Y. Reflection on Schur-Cohn matrices and Jury-Marden tables and classification of related unit-circle zero location criteria. Circ Syst Sig Process. 1996;15(1):111–136. doi: 10.1007/BF01187696
   Web of Science ®Google Scholar
• Schur I. Über potenzreihen, die in innern des einheitskreises beschränkt sind. J für die Reine und Angew Math. 1917;147:205–232. 1918;148: 122–145.
   Google Scholar
• Cohn A. Über die anzahl der wurzeln einer algebraischen gleichung in einem Kreise. Math Zeit. 1922;14:110–148. doi: 10.1007/BF01215894
   Google Scholar
• Fujiwara M. Über die algebraische Gleichungen, deren Wurzeln in einem Kreise order in einer Halbebene liegen. Math Z. 1926;24:161–169. doi: 10.1007/BF01216772
   Google Scholar
• Jury EI. The roles of Sylvester and Bezoutian matrices in the historical study of stability of linear discrete-time systems. IEEE Trans Circ Syst I. 1998;45(12):1233–1251. doi: 10.1109/81.736557
   Google Scholar
• Jury EI. A modified stability table for linear discrete systems. Proc IEEE. 1965;53:184–185. doi: 10.1109/PROC.1965.3612
   Google Scholar
• Jury EI. Modified stability table for 2-D digital filter. IEEE Trans Circ Syst. 1988;35:116–119. doi: 10.1109/31.1707
   Google Scholar
• Anderson PG, Garey MR, Heindel LE. Combinational aspects of deciding if all roots of a polynomial lie within the unit circle. Computing. 1976;16:293–304. doi: 10.1007/BF02252078
   Web of Science ®Google Scholar
• Bistritz Y. Fraction-free unit-circle stability tests. Circ Syst Sig Process. 2014;33:3783–3807. doi: 10.1007/s00034-014-9824-3
   Web of Science ®Google Scholar
• Premaratne K, Jury EI. On the Bistritz tabular form and its relationship with the Schur–Cohn minors and inner determinants. J Franklin Inst. 1993;330(1):165–182. doi: 10.1016/0016-0032(93)90028-S
   Web of Science ®Google Scholar
• Bistritz Y. Immittance-type tabular stability test for 2-D LSI systems based on a zero location test for 1-D complex polynomials. Circ Syst Sig Process. 2000;19(3):245–265. doi: 10.1007/BF01204577
   Web of Science ®Google Scholar
• Bistritz Y. On testing stability of 2-D discrete systems by a finite collection of 1-D stability tests. IEEE Trans Circ Syst I Fundam Theory Appl. 2002;49(11):1634–1638. doi: 10.1109/TCSI.2002.804540
   Google Scholar
• Bistritz Y, Lifshitz A. Bounds for resultants of univariate and bivariate polynomial. Linear Algebra Appl. 2010;432(8):1995–2005. doi: 10.1016/j.laa.2009.08.012
   Web of Science ®Google Scholar