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.