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Exact Matrix Completion via Convex Optimization
Matrix completion low-rank matrices convex optimization duality in optimization nuclear norm minimization random matrices noncommutative Khintchine inequality decoupling compressed sensing
2015/6/17
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. ...
A SINGULAR VALUE THRESHOLDING ALGORITHM FOR MATRIX COMPLETION
Nuclear norm minimization matrix completion singular value thresholding Lagrange dual function Uzawa’s algorithm and linearized Bregman iteration
2015/6/17
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxat...
The Power of Convex Relaxation:Near-Optimal Matrix Completion
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear norm minimization random matrices and techniques from random matrix theory free probability
2015/6/17
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applica...
Matrix Completion with Noise
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear-norm minimization oracle inequalities compressed sensing
2015/6/17
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data m...
Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements
Matrix completion The Dantzig selector oracle inequalities norm of random matrices convex optimization and semidefinite programming
2015/6/17
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
Formulae for the determination of the elements of the Eotvos matrix of the Earth's normal gravity field and a relation between normal and actual Gaussian curvature
Eotvos matrix normal gravity field equipotential surfaces Gauss curvature plumbline curvature
2011/9/1
Abstract: In this paper we form relations for the determination of the elements of the E\"otv\"os matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the ...
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenval...
On the canonical structure of regular pencil of singular matrix-functions
singular matrix-functions math
2010/11/15
The work is devoted to investigation of the canonical structure of regular, in domain of definition ${\cal U}\subseteq {\mathbb R}^{m}$, the pencil of matrix-functions $A(x)+\lambda B(x)$. It is supp...
On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix
On Jiang's asymptotic distribution correlation matrix
2010/11/19
Let $ \{X, X_{k,i}; i \geq 1, k \geq 1 \}$ be a double array of nondegenerate i.i.d. random variables and let $\{p_{n}; n \geq 1 \}$ be a sequence of positive integers such that $n/p_{n}$ is bounded a...
Using Hook Schur Functions to Compute Matrix Cocharacters
Using Hook Schur Functions Compute Matrix Cocharacters
2010/11/12
We use hook Schur functions to compute trace cocharacters of matrices in hooks. As an example we compute the cocharacters of 3 x 3 matrices in the one by two hook
The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann--Hilbert problems
multi-component 2D Toda hierarchy orthogonal polynomials Riemann--Hilbert problems
2010/4/7
We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresp...
Lp Solutions of Vector Refinement Equations with General Dilation Matrix
Lp Solutions Vector Refinement Equations General Dilation Matrix
2018/4/20
The purpose of this paper is to investigate the solutions of refinement equations of the form'(x) = X®2Zs a(®)'(Mx ¡ ®); x 2 Rs; where the vector of functions ' = ('1; :::; 'r)T is...
We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pen...
Application of Tree-like Structure of Graph to Matrix Analysis
Application Tree-like Structure Matrix Analysis
2010/11/1
Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking...