Differential resolvents of minimal order and weight.
Nahay, John Michael (2004)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “A partial factorization of the powersum formula.”
Differential resolvents of minimal order and weight.
Powersum formula for polynomials whose distinct roots are differentially independent over constants.
Nahay, John Michael (2002)
International Journal of Mathematics and Mathematical Sciences
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Powersum formula for differential resolvents.
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The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
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On a Theorem by Van Vleck Regarding Sturm Sequences
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In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences...
Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials
Irina Karelin, Leonid Lerer (2001)
International Journal of Applied Mathematics and Computer Science
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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...