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Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation
(2015-06)
Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts ...
A Feasible Method for Optimization with Orthogonality Constraints
(2010-11)
Minimization with orthogonality constraints (e.g., X'X = I) and/or spherical constraints (e.g., ||x||_2 = 1) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, ...
Dynamic Compressive Spectrum Sensing for Cognitive Radio Networks
(2011-01)
In the recently proposed collaborative compressive sensing, the cognitive radios (CRs) sense the occupied spectrum channels by measuring linear combinations of channel powers, instead of sweeping a set of channels sequentially. ...
Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions
(2012-03)
In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations ...
A Curvilinear Search Method for p-Harmonic Flows on Spheres
(2008-01)
The problem of finding p-harmonic flows arises in a wide range of applications including micromagnetics, liquid crystal theory, directional diffusion, and chromaticity denoising. In this paper, we propose an innovative ...
Trust, But Verify: Fast and Accurate Signal Recovery from 1-bit Compressive Measurements
(2010-11)
The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; ...
An Efficient Gauss-Newton Algorithm for Symmetric Low-Rank Product Matrix Approximatins
(2014-05)
We derive and study a Gauss-Newton method for computing the symmetric low-rank product (SLRP) XXT, where X / Rnkfor k<n, that is the closest approximation to a given symmetric matrix A / Rnn in Frobenius norm. When A=BTB ...
Solving a Low-Rank Factorization Model for Matrix Completion by a Non-linear Successive Over-Relaxation Algorithm
(2010-03)
The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value ...
Decentralized Jointly Sparse Optimization by Reweighted Lq Minimization
(2012-02)
A set of vectors (or signals) are jointly sparse if their nonzero entries are commonly supported on a small subset of locations. Consider a network of agents which collaborative recover a set of joint sparse vectors. This ...
An Alternating Direction Algorithm for Matrix Completion with Nonnegative Factors
(2011-01)
This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to nd nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates ...