Solving linear discrete ill-posed problems for third order tensor equations based on a tensor t-product has attracted much attention. But when the data tensor is produced continuously, current algorithms are not time-saving. Here, we propose an incremental tensor regularized least squares (t-IRLS) algorithm with the t-product that incrementally computes the solution to the tensor regularized least squares (t-RLS) problem with multiple lateral slices on the right-hand side. More specifically, we update its solution by solving a t-RLS problem with a single lateral slice on the right-hand side whenever a new horizontal sample arrives, instead of solving the t-RLS problem from scratch. The t-IRLS algorithm is well suited for large data sets and real time operation. Numerical examples are presented to demonstrate the efficiency of our algorithm.

翻译：解决基于 Exor t 产品 的 3 级 Exmor 方程式 的线性离散问题引起了人们的极大关注。 但是, 当数据 stror 持续生成时, 目前的算法不会节省时间 。 在这里, 我们建议使用 t 产品 递增 AROR 常规化最小方程式( t- IRLS) 算法, 逐渐计算出以右侧多个横向切片 的 ARLS 问题 的解决方案。 更具体地说, 我们通过在新的水平样本到达时解决右侧的 t- RLS 问题, 而不是从零开始解决 t- RLS 问题, 来更新其解决方案 。 t- IRLS 算法非常适合大型数据集和实时操作 。 数字示例展示了我们的算法的效率 。