منابع مشابه
A chain rule for multivariate divided differences
In this paper we derive a formula for divided differences of composite functions of several variables with respect to rectangular grids of points. Letting the points coalesce yields a chain rule for partial derivatives of multivariate functions. Math Subject Classification: 41A05, 65D05, 26A06
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Consider two differential operators L1 = ∑ aid i and L2 = ∑ bjd j with coefficients in a differential field, say C(t) with d = ∂ ∂t for example. If the ai and bj are constants, the condition for the existence of a solution y of L1(y) = L2(y) = 0 is that the resultant in X of the polynomials (in C[X]) ∑ aiX i and ∑ bjX j is zero. A natural question is: how one could extend this for the case of n...
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Schur’s transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we show that they satisfy a structure theorem which allows us to compute them with a type of Euclidean division. As a consequence, a fast algorithm based on a dich...
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It is a well known fact that the resultants are invariant under translation. We extend this fact to arbitrary composition (where a translation is a particular composition with a linear monic polynomial), and to arbitrary subresultants (where the resultant is the 0-th subresultant).
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2001
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00018-9