Interpolating polynomials from their values
نویسندگان
چکیده
منابع مشابه
Interpolating Polynomials from Their Values
A fundamental technique used by many algorithms in computer algebra is interpolating polynomials from their values. This paper discusses two algorithms for-solving this problem for sparse multivariate polynomials, anupdated version of a probabilistic one and a new deterministic techniqo" that uses some ideas due to Ben-Or and Tiwari (1988). In addition algorithms are presented for quickly findi...
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We shall take it as known that a polynomial of degree n has at most n distinct zeros (a proof is given in Lemma 1 below). Given n+1 distinct real numbers xj and any numbers αj (0 ≤ j ≤ n), there is a unique polynomial p of degree at most n satisfying p(xj) = αj (0 ≤ j ≤ n). The polynomial is unique, since if p1 and p2 were two such polynomials, then p1−p2 would be zero at each xj: since it has ...
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A set of monomials x a 0 ; : : : ; x ar is called interpolating with respect to a subset S of the nite eld F q , if it has the property that given any pairwise diierent elements x 0 ; : : : ; x r in S and any set of elements y 0 ; : : :; y r in F q there are elements c 0 ; : : :; c r in F q such that y h = P r j=0 c j x a j h for 0 h r. In this paper we address the question of determining inter...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1990
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(08)80018-1