The singular value decomposition (SVD) is a very useful technique for dealing with general dense matrix problems. Recent years, SVD has become a computationally viable tool for solving a wide variety of problems raised in many practical applications, such as least squares data fitting, image compression, facial recognition, principal component analysis, latent semantic analysis, and computing the 2-norm, condition number, and numerical rank of a matrix.
For more information, please refer “Jack Dongarra, Mark Gates, Azzam Haidar. The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale. 2018 SIAM Review, vol.60, No.4, pp.808-865”