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Code Generation for Polynomial Multiplication

2009
We discuss the family of "divide-and-conquer" algorithms for polynomial multiplication, that generalize Karatsuba's algorithm. We give explicit versions of transposed and short products for this family of algorithms and describe code generation techniques that result in high-performance implementations.
Ling Ding, Éric Schost
openaire   +1 more source

POLYNOMIALS WITH MULTIPLE ROOTS AT 1

International Journal of Number Theory, 2014
We prove that every polynomial P(x) = 1 + a1x + ⋯ + adxd∈ ℂ[x] has a root at x = 1 of order at most [Formula: see text], where ε > 0, provided that the quantities H*(P) = max1 ≤ j ≤ d|aj| and d/ log H*(P) are sufficiently large (the order of the root of P at x = 1 is zero if P(1) ≠ 0).
openaire   +2 more sources

Multiple Comparisons of Polynomial Distributions

Biometrical Journal, 1984
AbstractAsymptotically correct 90 and 95 percentage points are given for multiple comparisons with control and for all pair comparisons of several independent samples of equal size from polynomial distributions. Test statistics are the maxima of the X2‐statistics for single comparisons. For only two categories the asymptotic distributions of these test
openaire   +2 more sources

On the Multiplicative Property of Indicial Polynomials

Computational Mathematics and Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

FPGA Implementation of a Run-Time Configurable NTT-Based Polynomial Multiplication Hardware

Microprocessors and Microsystems, 2020
Erkay SAVAS   +2 more
exaly  

Bivariate Polynomial Codes for Secure Distributed Matrix Multiplication

IEEE Journal on Selected Areas in Communications, 2022
Jesus Gomez-Vilardebo   +2 more
exaly  

On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials

SIAM Journal on Computing, 1973
Michael S Paterson
exaly  

Sparse Polynomial Multiplication for Lattice-Based Cryptography With Small Complexity

Journal of Supercomputing, 2016
Sedat Akleylek, Erdem Alkım
exaly  

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