*Lyapunov-style proof of stability of quantized-error algorithm contrasts with averaging results for quantized-regressor algorithm. Helps to determine which algorithm is most appropriate in a given application.*

W. A. Sethares and C. R. Johnson, Jr., "A Comparison of Two Quantized State Adaptive Algorithms," *IEEE Trans. on Acoustics, Speech, and Signal Processing*, Vol. 37, No. 1, pp. 138-143, Jan. 1989.

*Averaging applied to the Constant Modulus Algorithm; gives first theoretical demonstration of when and why this algorithm "works."*

C. R. Johnson, Jr., S. Dasgupta, and W. A. Sethares, "Averaging Theory for Proof of Local Stability of Real CMA," *IEEE Trans. on Acoustics, Speech, and Signal Processing*, Vol. 36, No. 6, pp. 900-910, June 1988.

*Signed IIR algorithms explored in terms of a geometric criterion. Raises important general questions for communication standards such as ADPCM.*

C. R. Elevitch, W. A. Sethares, and C. R. Johnson, Jr., "Quiver Diagrams for Signed Adaptive Algorithms," *IEEE Trans. on Acoustics, Speech, and Signal Processin*g, Vol. 37, No. 2, pp. 227-235, Feb. 1989.

*This study amalgamates virtually all known adaptive algorithms (with linear filters on error and regressor) into a simple generic form. Uses averaging theory to derive concrete expressions for behavior, especially stability.*

W. A. Sethares, B. D. O. Anderson, C. R. Johnson, Jr., "Adaptive Algorithms with Filtered Regressor and Filtered Error," *Mathematics of Control, Signals, and Systems*, 2:381-403, 1989.

*This book chapter summarizes the three major ways that people analyze adaptive algorithms (the expected value, deterministic averaging, and ODE approaches), and contains applications in several signal processing areas.*

W. A. Sethares, The LMS Family, in *Efficient System Identification and Signal Processing Algorithms*, Ed. N. Kalouptsidis and S. Theodoridis, Springer-Verlag, 1993.

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