Accurate SVDs of Structured Matrices

Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices

Accurate SVDs of weakly diagonally dominant M-matrices

We present a new O(n 3) algorithm which computes the SVD of a weakly diagonally dominant M-matrix to high relative accuracy. The algorithm takes as an input the offdiagonal entries of the matrix and its row sums.

Superfast Divide-and-Conquer Method and Perturbation Analysis for Structured Eigenvalue Solutions

We present a superfast divide-and-conquer method for finding all the eigenvalues as well as all the eigenvectors (in a structured form) of a class of symmetric matrices with off-diagonal ranks or numerical ranks bounded by r, as well as the approximation accuracy of the eigenvalues due to off-diagonal compression. More specifically, the complexity is O(r2n logn) + O(rn log n), where n is the or...

Ac-loraks: Autocalibrated Low-rank Modeling of Local K-space Neighborhoods

Introduction: Low-rank modeling of local k-space neighborhoods (LORAKS) is a recent constrained MRI framework that can enable accurate image reconstruction from sparselyand unconventionally-sampled k-space data [1,2]. Specifically, Ref. [1] showed that the k-space data for MR images that have limited spatial support or slowly-varying image phase can be mapped into structured low-rank matrices, ...

A Preconditioned Hybrid SVD Method for Accurately Computing Singular Triplets of Large Matrices

The computation of a few singular triplets of large, sparse matrices is a challenging task, especially when the smallest magnitude singular values are needed in high accuracy. Most recent efforts try to address this problem through variations of the Lanczos bidiagonalization method, but algorithmic research is ongoing and without production level software. We develop a high quality SVD software...