Results 231 to 240 of about 51,455 (264)

Asymptotic Evaluation of Gauss Polynomials

Proceedings of the American Mathematical Society, 1982
An asymptotic evaluation is given for the polynomials G ( α
Gallagher, Patrick X., Ramsey, L. Thomas, Wells, Benjamin B.   +2 more
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Efficient Evaluation of Matrix Polynomials

2018
We revisit the problem of evaluating matrix polynomials and introduce memory and communication efficient algorithms. Our algorithms, based on that of Patterson and Stockmeyer, are more efficient than previous ones, while being as memory-efficient as Van Loan’s variant. We supplement our theoretical analysis of the algorithms, with matching lower bounds
Niv Hoffman, Oded Schwartz, Sivan Toledo
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Evaluation of the heuristic polynomial GCD

Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95, 1995
The Heuristic Polynomial GCD procedure (GCDHEU) is used by the Maple computer algebra system, but no other. Because Maple has an especially efficient kernel that provides fast integer arithmetic, but a relatively slower interpreter for non-kernel code, the GCDHEU routine is especially effective in that it moves much of the computation into “bignum ...
Hsin-Chao Liao, Richard J. Fateman
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Verifiable Evaluation of Private Polynomials

2013 Fourth International Conference on Emerging Intelligent Data and Web Technologies, 2013
Polynomial evaluation is an important tool in constructing many cryptographic protocols, such as proof of retrievability and verifiable keyword search. However, for the high degree polynomials derived from very large datasets, polynomial evaluation becomes an intractable problem, especially for resource limited devices.
Xu Ma, Fangguo Zhang, Jin Li 0002
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Evaluating a polynomial and its reverse

ACM SIGACT News, 1978
The 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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On the cost of evaluating polynomials and their derivatives

Computing, 1982
Reducing 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, 1972
For 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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A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems

IEEE Transactions on Fuzzy Systems, 2021
, Wen-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, 2022
Liping Zhang, Xin Ning, Weijun Li
exaly  

Evaluating polynomials

International Journal of Mathematical Education in Science and Technology, 1989
Howard C. Johnson, Robert M. Exner
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