## Accuracy and speed in computing the Chebyshev collocation derivative, Volume 4411Wai Sun Don, Alex Solomonoff, Brown University. Division of Applied Mathematics, Langley Research Center National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1991 - Mathematics - 36 pages |

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Alex Solomonoff algorithm for computing algorithm is fastest Breuer and Everson Brown University Chebyshev collocation method Chebyshev Polynomials Chebyshev spectral derivative collocation points computed accurately computing the Chebyshev computing the derivative cosine transform algorithm cosine transform subroutine covariance matrix Cray different algorithms differentiation matrix Division of Applied double precision error of u(x ESSL subroutines even-odd algorithm explicit loops fast Fourier transforms faster Fastest Algorithm FFT algorithm FFT-Recursion algorithms flipping on Cray-2 FORTRAN identities and flipping L2 norm LARCLIB library subroutine M-direction machine precision matrix elements matrix multiply algorithm matrix-vector multiplication algorithm minimum possible roundoff multiple FFT multiply algorithm MV MV ESSL MV Expl MV MXM NASA number of vector polynomial interpolation possible roundoff error reduce the roundoff relative error Rothman shows CPU single precision Slowest Algorithm small number solution Spectral Methods three algorithms transform-recursion algorithm Transform-Recursion Method trigonometric identity form vector being differentiated Vector N MV