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 MUL-DI 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.

中文翻译：

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具有缺失数据的可分离非线性模型的改进多方向迭代算法

多方向迭代（MUL-DI）算法是一种高效的大规模模型算法，它建立了最小二乘（LS）和梯度下降（GD）算法之间的理论联系。但是，它在每次迭代中都涉及到 Givens 变换和密集矩阵计算，这导致了繁重的计算工作。在这封信中，针对缺失数据的可分离非线性模型提出了一种改进的 MUL-DI 算法。使用对角矩阵设计了几个方向，并根据LS算法获得了它们对应的步长。与传统算法相比，本文提出的算法具有以下优点：（1）收敛速度更快；(2) 具有简单的成本函数；(3) 对条件数更加鲁棒；(4) 计算量较少。