Osculatory Rational Hermite-like Interpolation

In the domain of science and technology, there are a lot of nonlinear problems needed to be resolved. Rational approximation, one type of nonlinear approximation, is drawing more and more attentions recently. Compared to polynomial interpolations, it's more flexible and can describe physical character of functions more accurately although it is complex. In the past few years, the development of science and technology and the prevalence of computer become the powerful tools of the research of rational interpolation. The research of rational interpolation is going further and it shows some special advantages in applications.Continued fraction is an old branch of rational approximation. The related theories are getting rid of the stale and bringing forth the fresh incessantly. The work in this thesis is based on continued fraction theory. Combining continued fractions with polynomial functions, we construct a new osculatory continued fraction interpolation—osculatory rational Hermite-like interpolation. Its representation is simpler than that of Hermite polynomial interpolation and its computation is concise since the continued fraction's coefficients can be worked out by using Viscovatov algorithm. We also extend univariate osculatory rational Hermite-like interpolation to bivariate case.