Root separation for reducible monic quartics
Andrej Dujella, Tomislav Pejković (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Andrej Dujella, Tomislav Pejković (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Nikos E. Mastorakis (1996)
Kybernetika
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I. R. Shafarevich (1999)
The Teaching of Mathematics
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I. R. Shafarevich (2001)
The Teaching of Mathematics
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Miloš Kössler (1951)
Czechoslovak Mathematical Journal
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Henryk Górecki (2009)
International Journal of Applied Mathematics and Computer Science
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The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization...
Weinian Zhang (1997)
Annales Polonici Mathematici
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The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.
Christoph Schwarzweller (2017)
Formalized Mathematics
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In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].
J. L. Walsh (1926)
Mathematische Zeitschrift
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Stef Graillat, Philippe Langlois (2007)
RAIRO - Theoretical Informatics and Applications
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Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real...
Gallardo, Luis H. (2006)
Applied Mathematics E-Notes [electronic only]
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