In this article, we discuss the issue of computational complexity in singular value decomposition (SVD) and propose a novel approach to reduce computational effort while preserving accuracy. The SVD is a fundamental tool in linear algebra, but its computation can be time-consuming for large datasets. To address this challenge, we introduce fast low-rank modifications of the thin SVD decomposition.
Our approach leverages the idea of rank reduction, which involves approximating the original matrix with a lower-rank matrix while preserving its essential properties. By applying this technique to the thin SVD decomposition, we can significantly reduce computational complexity without sacrificing accuracy.
To illustrate our approach, we provide several examples and comparisons with existing methods. Our results show that our fast low-rank modifications of the thin SVD decomposition offer a more efficient alternative for large datasets while maintaining the same level of accuracy as traditional methods.
In summary, this article presents a novel approach to reduce computational complexity in singular value decomposition by exploiting rank reduction techniques. The proposed method offers a more efficient and accurate alternative for large datasets, making it an important contribution to the field of linear algebra and related applications.
Fast Low-Rank Modifications of Thin Singular Value Decomposition
