Surface Approximation and Interpolation via Matrix SVD

Robust Padé Approximation via SVD

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...

Deterministic Sparse Column Based Matrix Reconstruction via Greedy Approximation of SVD

Given a matrix A ∈ Rm×n of rank r, and an integer k < r, the top k singular vectors provide the best rank-k approximation to A. When the columns of A have specific meaning, it is desirable to find (provably) “good” approximations to Ak which use only a small number of columns in A. Proposed solutions to this problem have thus far focused on randomized algorithms. Our main result is a simple gre...

Large-Scale Nyström Kernel Matrix Approximation Using Randomized SVD

The Nyström method is an efficient technique for the eigenvalue decomposition of large kernel matrices. However, to ensure an accurate approximation, a sufficient number of columns have to be sampled. On very large data sets, the singular value decomposition (SVD) step on the resultant data submatrix can quickly dominate the computations and become prohibitive. In this paper, we propose an accu...

Column subset selection via sparse approximation of SVD

Given a real matrix A ∈ Rm×n of rank r, and an integer k < r, the sum of the outer products of top k singular vectors scaled by the corresponding singular values provide the best rank-k approximation Ak to A. When the columns of A have specific meaning, it might be desirable to find good approximations to Ak which use a small number of columns of A. This paper provides a simple greedy algorithm...

Seismic data interpolation and denoising using SVD-free low-rank matrix factorization