Levenberg Marquardt ( LM ) Algorithm 1 –

1 – Introduction Parameter estimation for function optimization is a well established problem in computing, as there are countless applications in practice. For this work, we will focus specifically in implementing a distributed and parallel implementation of the Levenberg Marquardt algorithm, which is a well established numerical solver for function approximation given a limited data set. Parameter estimation is required for robotic applications, such as estimating relationships between multiple viewpoints in computer vision, also, orbit determination in aerospace applications requires function optimization using numerical methods based on limited observations. However, there are multiple other applications such as signal processing, control theory, and telecommunications that require such solutions. The Levenberg Marquardt algorithm is an iterative solver that performs calculations to improve the estimate at each step, the iterations continue until an adequate bound is reached. This iterative nature will allow us to implement a distributed version for parallel systems through load balancing at each step. Although this method has demonstrated to be robust and efficient, when solving high-order non-linear systems, the process might diverge, since convergence is not guaranteed, and the initial parameter estimate becomes critical for convergence. These technical details about the levenberg Marquardt algorithm are essential when working with this technique for either the basic traditional single processor algorithm, or when working with a large dataset that requires a large cpu cluster with a distributed implementation. Initially, our most basic requirement is to implement a distributed algorithm that is consistent with the single CPU approach.