Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require O(mn) operations to solve min ‖b−Ax‖ where A is an m by n matrix. We present a modification of the LAPACK routine xGELSY that requires O(mnk) operations where k is the effective numerical rank of the matrix A. For low rank matrices the modification is an order of magnitude faster tha...

When nonlinear behavior must be considered in sensitivity analysis studies, one needs to approximate higher order derivatives of the response of interest with respect to all input data. This paper presents an application of a general reduced order method to constructing higher order derivatives of response of interest with respect to all input data. In particular, we apply the method to constru...

We compute the circular Wilson loop ofN = 4 SYM theory at large N in the rank k symmetric and antisymmetric tensor representations. Using a quadratic Hermitian matrix model we obtain expressions for all values of the ’t Hooft coupling. At large and small couplings we give explicit formulae and reproduce supergravity results from both D3 and D5 branes within a systematic framework. 1. Background...

We consider one bit matrix completion under rank constraint. We present an estimator based on rank constrained maximum likelihood estimation, and an e cient greedy algorithm to solve it approximately based on an extension of conditional gradient descent. The output of the proposed algorithm converges at a linear rate to the underlying true low-rank matrix up to the optimal statistical estimatio...

In this paper, we propose novel gossip algorithms for the low-rank decentralized matrix completion problem. The proposed approach is on the Riemannian Grassmann manifold that allows local matrix completion by different agents while achieving asymptotic consensus on the global low-rank factors. The resulting approach is scalable and parallelizable. Our numerical experiments show the good perform...

This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is constructed based on interpolative low-ra...

We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well– posedness of the problem, we impose a joint low rank structure, wherein each component matrix is low rank and the latent space of the low rank factors corresponding to each entity is shared across the entire c...

Polymer-clay nano-composite materials, in which nano-meter thick layers of clay dispersed in polymer matrix, have generally higher mechanical properties than normal polymeric materials. A new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. The total elastic modulus of nano-composite is evaluated.  Numerical r...

Polymer-clay nano-composite materials, in which nano-meter thick layers of clay dispersed in polymer matrix, have generally higher mechanical properties than normal polymeric materials. A new three-dimensional unit cell model has been developed for modeling three constituent phases including inclusion, interphase and matrix. The total elastic modulus of nano-composite is evaluated.  Numerical r...

We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of the matrix corresponds to a frame in the image time series; the matrix is highly low-rank since the frames are highly correlated. Similarly the non-zero loca...