Modified Multi-Direction Iterative Algorithm for Separable Nonlinear Models With Missing Data

Abstract

Multi-direction iterative (MUL-DI) algorithm is an efficient algorithm for large-scale models, and it establishes a theoretical linkage between least squares (LS) and gradient descent (GD) algorithms. However, it involves Givens transformation and dense matrix calculation in each iteration, which leads to heavy computational efforts. In this letter, a modified MULDI algorithm is proposed for separable nonlinear models with missing data. Several directions are designed using a diagonal matrix, and their corresponding step-sizes are obtained based on LS algorithm. Compared with the traditional algorithms, the algorithm proposed in this letter has the following advantages: (1) has a faster convergence rate; (2) has a simple cost function; (3) is more robust to the condition number; (4) has less computational efforts. A simulation example shows the effectiveness of the modified MUL-DI algorithm.