Results 271 to 280 of about 17,255,193 (320)

On the Parallel Evaluation of Multivariate Polynomials

SIAM Journal on Computing, 1978
We prove that any multivariate polynomial P of degree d that can be computed with $C(P)$ multiplications-divisions can be computed in $O(\log d \cdot \log C(P))$ parallel steps and $O(\log d)$ parallel multiplicative steps.
openaire   +2 more sources

Homomorphic polynomial evaluation using Galois structure and applications to BFV bootstrapping

IACR Cryptology ePrint Archive, 2023
Hiroki Okada, Rachel Player, Simon Pohmann   +2 more
semanticscholar   +1 more source

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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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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Flashproofs: Efficient Zero-Knowledge Arguments of Range and Polynomial Evaluation with Transparent Setup

IACR Cryptology ePrint Archive, 2022
Nan Wang, S. Chau
semanticscholar   +1 more source

Algorithms for accurate, validated and fast polynomial evaluation

, 2009
We survey a class of algorithms to evaluate polynomials with floating point coefficients and for computation performed with IEEE-754 floating point arithmetic. The principle is to apply, once or recursively, an error-free transformation of the polynomial
S. Graillat, P. Langlois, N. Louvet
semanticscholar   +1 more source

Unconditionally Secure Oblivious Polynomial Evaluation: A Survey and New Results

Journal of Computational Science and Technology, 2022
Louis Cianciullo, Hossein Ghodosi
semanticscholar   +1 more source

Evaluation of Polynomials

1993
In this chapter, we consider the evaluation of a polynomial function of a single variable. We usually compute the value of an arithmetic function by replacing each arithmetic operation by its corresponding floating-point machine operation (see Section 3.5). Roundoff errors and cancellations sometimes cause the calculated result to be drastically wrong.
Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks   +3 more
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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
openaire   +1 more source

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
openaire   +1 more source