Convergence Properties of Fixed-Point Harmonic Balance Algorithms

A necessary condition for the local convergence of Borich's fixed point harmonic balance algorithm is derived. The delineation of regions with different convergence properties is then performed using convergence maps. These maps explain the poor convergence and non-convergence that is exhibited by fixed point harmonic balance algorithms in practical applications. A connection between optimal fixed point harmonic balance and conventional harmonic balance is established. This provides a series of insights into ways of improving the generality and performance of fixed point harmonic balance algorithms.