Algebraic Expression of Solutions for Harmonic Balance Method using Error Bound

摘要

The solutions of the HB method are zero dimensional ideal. In order to obtain the zero dimensional ideal using Grobner base of lexicographic order, we need tremendously large computational cost. On the other hand, the error bound of the HB method with n unknowns is represented by n - 1 dimensional ideal. That is, the error bound is represented by only one equation. The fact indicates that the computational cost of calculating the error bound is less than that of solving the HB equation for computer algebra. This paper proposes to use the error bounds for the expression of solutions for the HB equations.