New adaptive-filtering algorithms, also known as adaptation algorithms, are proposed. The new algorithms can be broadly classified into two categories, namely, steepest-descent and Newton-type adaptation algorithms. Several new methods have been used to bring about improvements regarding the speed of convergence, steady-state misalignment, robustness with respect to impulsive noise, re-adaptation capability, and computational load of the proposed algorithms.;In chapters 2, 3, and 8, several adaptation algorithms are developed that belong to the steepest-descent family. The algorithms of chapters 2 and 3 use two error bounds with the aim of reducing the computational load, achieving robust performance with respect to impulsive noise, good tracking capability and significantly reduced steady-state misalignment. The error bounds can be either prespecified or estimated using an update formula that incorporates a modified variance estimator. Analyses pertaining to the steady-state mean-square error (MSE) of some of these algorithms are also presented. The algorithms in chapter 8 use a so-called iterative/shrinkage method to obtain a variable step size by which improved convergence characteristics can be achieved compared to those in other state-of-the-art competing algorithms.;Several adaptation algorithms that belong to the Newton family are developed in chapters 4-6 with the aim of achieving robust performance with respect to impulsive noise, reduced steady-state misalignment, and good tracking capability without compromising the initial speed of convergence. The algorithm in chapter 4 imposes a bound on the L1 norm of the gain vector in the crosscorrelation update formula to achieve robust performance with respect to impulsive noise in stationary environments. In addition to that, a variable forgetting factor is also used to achieve good tracking performance for applications in nonstationary environments. The algorithm in chapter 5 is developed to achieve a reduced steady-state misalignment and improved convergence speed and a reduced computational load. The algorithm in chapter 6 is essentially an extension of the algorithm in chapter 5 designed to achieve robust performance with respect to impulsive noise and reduced computational load. Analyses concerning the asymptotic stability and steady-state MSE of these algorithms are also presented.;An algorithm that minimizes Reny's entropy of the error signal is developed in chapter 7 with the aim of achieving faster convergence and reduced steady-state misalignment compared to those in other algorithms of this family.;Simulation results are presented that demonstrate the superior convergence characteristics of the proposed algorithms with respect to state-of-the-art competing algorithms of the same family in network-echo cancelation, acoustic-echo cancelation, system-identification, interference-cancelation, time-series prediction, and time-series filtering applications. In addition, simulation results concerning system-identification applications are also used to verify the accuracy of the MSE analyses presented.
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