Year: 2011
Type: article
Abstract: In a recent paper, Lima, Panario, and Wang have provided a new method to multiply polynomials expressed in Chebyshev basis which reduces the total number of multiplication for small degree polynomials. Although their method uses Karatsuba's multiplication, a quadratic number of operations are still needed. In this paper, we extend their result by providing a complete reduction to polynomial multiplication in monomial basis, which therefore offers many subquadratic methods. Our reduction scheme does not rely on basis conversions and we demonstrate that it is efficient in practice. Finally, we show a linear time equivalence between the polynomial multiplication problem under monomial basis and under Chebyshev basis.
Source: IEEE Transactions on Computers
DOI: 10.1109/tc.2011.110
Author: Pascal Giorgi
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2048225141