ERROR-ENERGY BOUNDS FOR ADAPTIVE GRADIENT ALGORITHMS

The paper establishes robustness, optimality, and convergence properti es of the widely used class of instantaneous-gradient adaptive algorit hms, The analysis is carried out in a purely deterministic framework a nd assumes no a priori statistical information, It employs the Cauchy- Schwarz inequality for vectors in an Euclidean space and derives local and global error-energy bounds that are shown to highlight, as well a s explain, relevant aspects of the robust performance of adaptive grad ient filters (along the lines of H-infinity theory).