Formulations,algorithms and applications on barycentric interpolation in 1D

The advantages of barycentric interpolation formulations in computation are small number of floating point operations(flops) and good numerical stability.Adding a new data pair,the barycentric interpolation formula don't require renew computation all basis functions.It can avoid the oscillation of Lagrange interpolation by using barycentric interpolation formulations and second kind of Chebyshev points as interpolating points.In barycentric interpolation formulations,the different weight corresponds to different type interpolation.The most of these interpolation are barycentric rational interpolation.The barycentric rational interpolations have more accuracy than the polynomial interpolation in computation.In this paper,reviewed are the formulations,distribution of interpolating points,interpolating accuracy and applications of barycentric interpolation.And presented are the formula of interpolation,algorithms and some numerical examples.