Incremental tensor regularized least squares with multiple right-hand sides

TL;DR

This paper introduces an incremental tensor regularized least squares algorithm that efficiently updates solutions for large, real-time tensor problems with multiple right-hand sides, avoiding recomputation from scratch.

Contribution

The paper presents a novel incremental algorithm for tensor regularized least squares that updates solutions efficiently as new data arrives, suitable for large-scale and real-time applications.

Findings

The t-IRLS algorithm significantly reduces computation time.

Numerical examples confirm the efficiency and practicality of the method.

The approach is effective for large and continuously growing data sets.

Abstract

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.