Results 11 to 20 of about 51,455 (264)
EVALUATION PROPERTIES OF SYMMETRIC POLYNOMIALS [PDF]
International Journal of Algebra and Computation, 2006 By the fundamental theorem of symmetric polynomials, if P ∈ ℚ[X1,…,Xn] is symmetric, then it can be written P = Q(σ1,…,σn), where σ1,…,σn are the elementary symmetric polynomials in n variables, and Q is in ℚ[S1,…,Sn]. We investigate the complexity properties of this construction in the straight-line program model, showing that the complexity of ...
Pierrick Gaudry +2 more
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Generalized monotone triangles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In a recent work, the combinatorial interpretation of the polynomial $\alpha (n; k_1,k_2,\ldots,k_n)$ counting the number of Monotone Triangles with bottom row $k_1 < k_2 < ⋯< k_n$ was extended to weakly decreasing sequences $k_1 ≥k_2 ≥⋯≥k_n$.
Lukas Riegler
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Evaluating Fishing Capacity Based on DEA and Regression Analysis of China’s Offshore Fishery
Journal of Marine Science and Engineering, 2021 The analysis of offshore fishing capacity is of great significance and practical value to the sustainable utilization and conservation of marine fishery resources. Based on the 2004–2020 China Fishery Statistical Yearbook, data envelopment analysis (DEA)
Shuang Liu +4 more
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Systolic evaluation of polynomial expressions [PDF]
IEEE Transactions on Computers, 1990 Two types of organizations are presented for frame buffers of m*m pixels: one is a single wavefront complex cell array requiring O(m/sup 2/n) space and the other is a simple cell multiple wavefront array with O(m/sup 2/) area and O(n/sup 2/) wavefronts.
Mathias, PC, Patnaik, LM
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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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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 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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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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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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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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