Search Methods
Behrouz Farhang‐Boroujeny · 2013
This chapter discusses two gradient-based iterative methods for searching the performance surface of a transversal Wiener filter to find the tap weights that correspond to its minimum point. These include method of steepest descent and Newton's method. A learning curve of the steepest-descent algorithm consists of a sum of N exponentially decaying terms, each of which corresponds to one of the modes of convergence of the algorithm. The chapter shows that the performance of the steepest-descent algorithm is highly dependent on the eigenvalues of the correlation matrix R. Further insight into the operation of Newton's algorithm is developed by giving an alternative derivation of that. This derivation uses the Karhunen-Loéve transform (KLT). It shows that Newton's algorithm may be viewed as a steepest-descent algorithm for the transformed input signal. Controlled Vocabulary Terms eigenvalues and eigenfunctions; gradient methods; iterative methods; Karhunen-Loeve transforms; Wiener filters