Study On Method Of Matrixvalues Rational Interpolation Function

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.Binary matrix rational interpolation function constructed by Thiele-type structure is ( mn + m+n,2[(mn+m+n)/2]) type rational function and its degree is relatively high. Therefore, we construct a function to reduce its degree which is called Lagrange-type interpolation function. And the denominator degree can be determined according to the needs. We also discuss the poles and unattainable points issues. Under certain conditions we can also reduce the numerator degree, It is simple to calculate and convenient in application.The matrix values of rational functions structured by section 4.4 go a step further, It is obtained based on block rational interpolation.It is not difficult to find after analysis, Its denominator is positive number in the real domain , So it does not exist the question of poles itself, we can find that the times of numerator and denominator are relatively small by examples, obtain more convenient operation.