Sturm root counting using chebyshev expansion

Abstract

The Sturm's root counting method by the floating point calculation was studied to solve real roots of a real algebraic equation of high degree. To reduce the effects of round-off errors, polynomials are represented by the coefficients of Chebyshev polynomials instead of monomials. In the Sturm sequence calculation, the quotients are stored instead of remainders. The values of remainders at a given abscissa to count their sign variations are calculated from the stored sequence of quotients. This approach reduces the space and the number of arithmetic operations. Some experiments was made using the FP numbers.