The trapezoidal method of steepest-descent and its application to adaptive filtering

The method of steepest-descent is re-visited in continuous time. It is shown that the continuous time version is a vector differential equation the solution of which is found by integration. Since numerical integration has many forms, we show an alternative to the conventional solution by using a Trapezoidal integration solution. This in turn gives a slightly modified least-mean squares (LMS) algorithm. Keyword: Steepest-Descent, Least-mean squares (LMS), Adaptive filters.