Results 21 to 30 of about 17,255,193 (320)
Mathematics, 2023 The evaluation of objective functions and component reliability in the optimisation of structural-acoustic systems with random and interval variables is computationally expensive, especially when strong nonlinearity exhibits between the response and ...
Shengwen Yin +3 more
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A graph polynomial for independent sets of bipartite graphs [PDF]
, 2010 We introduce a new graph polynomial that encodes interesting properties of graphs, for example, the number of matchings and the number of perfect matchings.
Ge, Qi, Stefankovic, Daniel
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Evaluations of Topological Tutte Polynomials [PDF]
Combinatorics, Probability and Computing, 2014 We find new properties of the topological transition polynomial of embedded graphs, Q(G). We use these properties to explain the striking similarities between certain evaluations of Bollobás and Riordan's ribbon graph polynomial, R(G), and the topological Penrose polynomial, P(G).
Joanna A. Ellis-Monaghan, Iain Moffatt
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On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 C. Merino [Electron. J. Combin. 15 (2008)] showed that the Tutte polynomial of a complete graph satisfies $t(K_{n+2};2,-1)=t(K_n;1,-1)$. We first give a bijective proof of this identity based on the relationship between the Tutte polynomial and the ...
Andrew Goodall +3 more
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On the evaluation of modular polynomials [PDF]
The Open Book Series, 2013 We present two algorithms that, given a prime ell and an elliptic curve E/Fq, directly compute the polynomial Phi_ell(j(E),Y) in Fq[Y] whose roots are the j-invariants of the elliptic curves that are ell-isogenous to E. We do not assume that the modular polynomial Phi_ell(X,Y) is given.
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Provably faithful evaluation of polynomials [PDF]
Proceedings of the 2006 ACM symposium on Applied computing, 2006 We provide sufficient conditions that formally guarantee that the floating-point computation of a polynomial evaluation is faithful. To this end, we develop a formalization of floating-point numbers and rounding modes in the Program Verification System (PVS).
Boldo, Sylvie, Muñoz, César
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Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
Nuclear Physics B, 2022 We study the Gaudin models associated with gl(1|1). We give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules.
Kang Lu
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Evaluations of Graph Polynomials [PDF]
, 2008 A graph polynomial $p(G, \bar{X})$ can code numeric information about the underlying graph G in various ways: as its degree, as one of its specific coefficients or as evaluations at specific points $\bar{X}= \bar{x}_0$. In this paper we study the question how to prove that a given graph parameter, say *** (G ), the size of the maximal clique of G ...
Benny Godlin +2 more
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Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs [PDF]
, 2015 A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program (ABP) where each variable occurs in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly
Gurjar, Rohit +3 more
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Polynomial Evaluation Schemes [PDF]
Mathematics of Computation, 1975 An attempt is made to define a polynomial evaluation algorithm that is more resistant to accumulated round-off error than the schemes of Horner and Clenshaw under conditions of floating-point arithmetic. An algorithm is presented which generally compares favorably with both.
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