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@article{Townsend:2018:mcom/3277,
author = {Townsend, A and Webb, M and Olver, S},
doi = {mcom/3277},
journal = {Mathematics of Computation},
pages = {1913--1934},
title = {Fast polynomial transforms based on Toeplitz and Hankel matrices},
url = {http://dx.doi.org/10.1090/mcom/3277},
volume = {87},
year = {2018}
}

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TY  - JOUR
AB  - Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive algorithms with an observed complexity of $ \smash {\mathcal {O}(N\log ^2 \! N)}$, based on the fast Fourier transform, for converting coefficients of a degree $ N$ polynomial in one polynomial basis to coefficients in another. Numerical results show that this approach is competitive with state-of-the-art techniques, requires no precomputational cost, can be implemented in a handful of lines of code, and is easily adapted to extended precision arithmetic.
AU  - Townsend,A
AU  - Webb,M
AU  - Olver,S
DO  - mcom/3277
EP  - 1934
PY  - 2018///
SN  - 0025-5718
SP  - 1913
TI  - Fast polynomial transforms based on Toeplitz and Hankel matrices
T2  - Mathematics of Computation
UR  - http://dx.doi.org/10.1090/mcom/3277
VL  - 87
ER  -

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