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Evaluating a polynomial and its reverse
ACM SIGACT News, 1978The reverse of an n th degree polynomial p(x) is rev(p) (x) = x n p(x -1 ). We show that one can evaluate p and rev(p) in only n+0(log n) multiplications modulo {x -1 }. The method uses an algorithm to evaluate reciprocal polynomials of degree n
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Evaluation of orthogonal polynomial compression
The Journal of the Acoustical Society of America, 1991In orthogonal polynomial compression, the short-term speech spectrum is first approximated by a family of orthogonal polynomials. The coefficients of each polynomial, which vary over time, are then adjusted in terms of their average value and range of variation.
H, Levitt, A C, Neuman
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On the cost of evaluating polynomials and their derivatives
Computing, 1982Reducing the number of multiplications for the evaluation of a polynomial and its derivatives does not necessarily mean that one should expect a commensurate reduction of the total cost of computation. In this paper we present a cost analysis for a family of algorithms, which computes all derivatives of a polynomial in 3n−2 multiplications or divisions.
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Explicit Evaluation of Certain Polynomials
SIAM Journal on Mathematical Analysis, 1972For real nonzero k, put \[ S_m (k) = \frac{1}{2}\sum _{n = 0}^\infty {\alpha _n^{ - m - 2} } ,\qquad T_m (k) = \frac{1}{2}\sum _{n = 0}^\infty {\beta _n^{ - 2m - 2} } ,\] where $\alpha _n $ runs through the nonzero roots of $\tan \alpha = k\alpha $ and $\beta _n $ runs through the roots of $k\cot \beta + \beta = 0$. Liron [2, pp.
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Verifiable and Private Oblivious Polynomial Evaluation
Workshop in Information Security Theory and Practice, 2019Hardik Gajera +4 more
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Unconditionally Secure Distributed Oblivious Polynomial Evaluation
International Conference on Information Security and Cryptology, 2018Louis Cianciullo, Hossein Ghodosi
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Oblivious Polynomial Evaluation and Secure Set-Intersection from Algebraic PRFs
Journal of Cryptology, 2015Carmit Hazay
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Information-theoretically secure oblivious polynomial evaluation in the commodity-based model
International Journal of Information Security, 2014Rafael Tonicelli +6 more
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A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems
IEEE Transactions on Fuzzy Systems, 2021Wen-Bo Xie, Hak-Keung Lam
exaly
Encoder-X: Solving Unknown Coefficients Automatically in Polynomial Fitting by Using an Autoencoder
IEEE Transactions on Neural Networks and Learning Systems, 2022Guojun Wang, Weijun Li, Linjun Sun
exaly