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The current implementation of the T-REXI (Terry Haut's et al. REXI) coefficients only approximate the real coefficients of exp(ix) accurately. This is OK for a precision which is a little bit higher than single precision (See Schreiber et al. paper on "Beyond scalability limitation...").
The reason why this works is rather accidentally: the imaginary values of the rational approximation of the Gaussian basis function should be actually garbage data. However, this resembles the imaginary coefficients of exp(ix) quite well. Therefore it was working so far.
The suggested fix increases the number of poles by a factor of 2, but halving them again leads to the same number of poles required for T-REXI. The benefits are that one can how really get down close to double precision accuracy as it was also the case in the original T-REXI paper (T. Haut et al.).
The text was updated successfully, but these errors were encountered:
The current implementation of the T-REXI (Terry Haut's et al. REXI) coefficients only approximate the real coefficients of exp(ix) accurately. This is OK for a precision which is a little bit higher than single precision (See Schreiber et al. paper on "Beyond scalability limitation...").
The reason why this works is rather accidentally: the imaginary values of the rational approximation of the Gaussian basis function should be actually garbage data. However, this resembles the imaginary coefficients of exp(ix) quite well. Therefore it was working so far.
The suggested fix increases the number of poles by a factor of 2, but halving them again leads to the same number of poles required for T-REXI. The benefits are that one can how really get down close to double precision accuracy as it was also the case in the original T-REXI paper (T. Haut et al.).
The text was updated successfully, but these errors were encountered: