1,341 research outputs found
Performance Evaluation of an Extrapolation Method for Ordinary Differential Equations with Error-free Transformation
The application of error-free transformation (EFT) is recently being
developed to solve ill-conditioned problems. It can reduce the number of
arithmetic operations required, compared with multiple precision arithmetic,
and also be applied by using functions supported by a well-tuned BLAS library.
In this paper, we propose the application of EFT to explicit extrapolation
methods to solve initial value problems of ordinary differential equations.
Consequently, our implemented routines can be effective for large-sized linear
ODE and small-sized nonlinear ODE, especially in the case when harmonic
sequence is used
Constraining the helium abundance with CMB data
We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160 < Y_p < 0.501 (at 68% c.l.). We analyse the impact on the baryon abundance as measured by CMB and discuss the implications for big bang nucleosynthesis. We identify and discuss correlations between the helium mass fraction and both the redshift of reionization and the spectral index. We forecast the precision of future CMB observations, and find that Planck alone will measure Y_p with error-bars of 5%. We point out that the uncertainty in the determination of the helium fraction will have to be taken into account in order to correctly estimate the baryon density from Planck-quality CMB data
Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic
23 pagesWe introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We aim at always obtaining correctly-rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value
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