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polynomial functionals
, 2012
"... Sparse spectral approximations for computing polynomial functionals ..."
Minimizing polynomial functions
 PROCEEDINGS OF THE DIMACS WORKSHOP ON ALGORITHMIC AND QUANTITATIVE ASPECTS OF REAL ALGEBRAIC GEOMETRY IN MATHEMATICS AND COMPUTER SCIENCE
, 2003
"... We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves su ..."
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Cited by 60 (3 self)
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We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
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Cited by 580 (6 self)
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#erential or di#erence equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between di#erent classes of orthogonal polynomials listed in the Askeyscheme. In chapter
Polynomial functions on bounded chains
 IFSAEUSFLAT
, 2009
"... We are interested in representations and characterizations of lattice polynomial functions f: L n → L, where L is a given bounded distributive lattice. In an earlier paper [4, 5], we investigated certain representations and provided various characterizations of these functions both as solutions of c ..."
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We are interested in representations and characterizations of lattice polynomial functions f: L n → L, where L is a given bounded distributive lattice. In an earlier paper [4, 5], we investigated certain representations and provided various characterizations of these functions both as solutions
LOCAL POLYNOMIAL FUNCTIONS ON LATTICES
"... K. A. Baker and A. F. Pixley [ 1] proved that for any finite lattice L a function f: L n • L is a polynomial function (alias algebraic function) if and only if all diagonal sublattices of the square (alias reflexive compatible binary relations) are closed under f. For infinite lattices, this conditi ..."
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K. A. Baker and A. F. Pixley [ 1] proved that for any finite lattice L a function f: L n • L is a polynomial function (alias algebraic function) if and only if all diagonal sublattices of the square (alias reflexive compatible binary relations) are closed under f. For infinite lattices
The polynomial functions on Frobenius complements
 Acta Sci. Math. (Szeged
, 2006
"... Abstract. We determine the number of unary polynomial functions on all Frobenius complements and on all finite solvable groups all of whose abelian subgroups are cyclic. 1. Notation and results Let (G, ·) be a group. A unary polynomial function p: G → G is a function that can be written in the form ..."
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Cited by 2 (2 self)
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Abstract. We determine the number of unary polynomial functions on all Frobenius complements and on all finite solvable groups all of whose abelian subgroups are cyclic. 1. Notation and results Let (G, ·) be a group. A unary polynomial function p: G → G is a function that can be written in the form
Homomorphic signatures for polynomial functions
, 2010
"... We construct the first homomorphic signature scheme that is capable of evaluating multivariate polynomials on signed data. Given the public key and a signed data set, there is an efficient algorithm to produce a signature on the mean, standard deviation, and other statistics of the signed data. Prev ..."
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Cited by 56 (4 self)
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We construct the first homomorphic signature scheme that is capable of evaluating multivariate polynomials on signed data. Given the public key and a signed data set, there is an efficient algorithm to produce a signature on the mean, standard deviation, and other statistics of the signed data
Optimization of polynomial functions
 Can. Math. Bull
"... Recently progress has been made in the development of algorithms for optimizing polynomials. The main idea being stressed is that of reducing the problem to an easier problem involving semidefinite programming [18]. It seems that in many cases the method dramatically outperforms other existing metho ..."
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Cited by 23 (4 self)
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to Putinar [13] to prove that the method produces the exact minimum in the compact case. In the general case it produces a lower bound for the minimum. The ideas involved come from three branches of mathematics: algebraic geometry (positive polynomials), functional analysis (the moment problem
Piecewise Polynomial Functions . . .
, 2006
"... Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region �) of R d. The set of splines of degree at most k forms a vector space C r k (∆). Moreover, a nice way to study C r k (∆) is to embed ∆ in Rd+1, and form the co ..."
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Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region �) of R d. The set of splines of degree at most k forms a vector space C r k (∆). Moreover, a nice way to study C r k (∆) is to embed ∆ in Rd+1, and form
ON THE GROUP OF POLYNOMIAL FUNCTIONS IN A GROUP
, 2007
"... Abstract. Let G be a group and let n be a positive integer. A polynomial function in G is a function from G n to G of the form (t1,..., tn) → f(t1,..., tn), where f(x1,..., xn) is an element of the free product of G and the free group of rank n freely generated by x1,..., xn. There is a natural def ..."
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Abstract. Let G be a group and let n be a positive integer. A polynomial function in G is a function from G n to G of the form (t1,..., tn) → f(t1,..., tn), where f(x1,..., xn) is an element of the free product of G and the free group of rank n freely generated by x1,..., xn. There is a natural
Results 1  10
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554,407