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Error-energy bounds for adaptive gradient algorithms

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2 Author(s)
Sayed, A.H. ; Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA ; Rupp, M.

The paper establishes robustness, optimality, and convergence properties of the widely used class of instantaneous-gradient adaptive algorithms. The analysis is carried out in a purely deterministic framework and 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 as explain, relevant aspects of the robust performance of adaptive gradient filters (along the lines of H theory)

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Signal Processing, IEEE Transactions on  (Volume:44 ,  Issue: 8 )