Low-Rank Matrix Approximations Do Not Need a Singular Value Gap
Low-Rank Matrix Approximations Do Not Need a Singular Value Gap is a scholarly work, published in 2019 in ''SIAM Journal on Matrix Analysis and Applications''. The main subjects of the publication include pure mathematics, matrix, singular value, matrix norm, projector, applied mathematics, subspace topology, mathematical analysis, Total least squares, singular value decomposition, compressed sensing, rank, low-rank approximation, multiplicative function, mathematics, norm, numerical linear algebra, and approximations of π. The authors show that the low-rank approximation errors, in the two-norm, Frobenius norm and more generally, any Schatten p-norm, are insensitive to additive rank-preserving perturbations in the projector basis; and to matrix perturbations that are additive or change the number of columns (including multiplicative perturbations).