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- W2964132515 abstract "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<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O left-parenthesis upper N log squared upper N right-parenthesis><mml:semantics><mml:mrow><mml:mrow class=MJX-TeXAtom-ORD><mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi></mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>N</mml:mi><mml:msup><mml:mi>log</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mspace width=negativethinmathspace /><mml:mi>N</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>mathcal {O}(Nlog ^2 ! N)</mml:annotation></mml:semantics></mml:math></inline-formula>, based on the fast Fourier transform, for converting coefficients of a degree<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper N><mml:semantics><mml:mi>N</mml:mi><mml:annotation encoding=application/x-tex>N</mml:annotation></mml:semantics></mml:math></inline-formula>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." @default.
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- W2964132515 date "2017-11-06" @default.
- W2964132515 modified "2023-09-26" @default.
- W2964132515 title "Fast polynomial transforms based on Toeplitz and Hankel matrices" @default.
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