When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the EckartYoung-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove a generalization of the Eckart-Young-Mirsky theorem under all unitarily invari...

The truncated singular value decomposition (TSVD) is a popular method for solving linear discrete ill-posed problems with small to moderately sized matrix A. This replaces the A by closest Ak of low rank k, and then computes minimal norm solution system equations rank-deficient so obtained. modified TSVD (MTSVD) improves method, replacing that closer than in unitarily invariant has same spectra...

Truncated singular value decomposition (TSVD) is a popular method for solving linear discrete ill-posed problems with a small to moderately sized matrix A. Regularization is achieved by replacing the matrix A by its best rank-k approximant, which we denote by Ak. The rank may be determined in a variety of ways, e.g., by the discrepancy principle or the L-curve criterion. This paper describes a ...