Abstract
Hybrid algorithm is formed by combining the symbolic methods with the numerical methods. Recently we have proposed a hybrid integration algorithm which calculates indefinite integral of a rational function with floating-point number coefficients. In this paper, the hybrid integration algorithm is extended to treat some kinds of functions and sets of data. In this method, the integrand is approximated by a rational function. In higher order rational function approximation, unnecessary zeros often occur in the denominator polynomial. We propose an algorithm that removes unnecessary zeros by the method of approximate gcd of the numerator and the denominator polynomials. Rational functions without these zeros are integrated easily.
