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Let M be a random nα × n matrix of rank r ≪ n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(r ...
Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix
Abel Inversion Bernstein Polynomials Almost Bernstein Operational Matrix Of Integration Noise Resistance
2013/1/30
A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier pr...
Computing the Moore-Penrose Inverse of a Matrix Through Symmetric Rank-One Updates
Finite Recursive Algorithm Moore-Penrose Inverse Symmetric Rank-One Update
2013/1/30
This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The compu...
Finite Projective Geometry based Fast, Conflict-free Parallel Matrix Computations
Distributed Computing Parallel Algorithms Parallel Processing
2011/9/29
Abstract: Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for so...
Divide-and-Conquer Matrix Factorization
Divide-and-Conquer Matrix Factorization Numerical Analysis
2011/9/29
Abstract: This work introduces SubMF, a parallel divide-and-conquer framework for noisy matrix factorization. SubMF divides a large-scale matrix factorization task into smaller subproblems, solves eac...
Sharp bounds on the rate of convergence of the empirical covariance matrix
Sharp bounds rate of convergence empirical covariance matrix
2011/1/17
Let X1, . . . ,XN ∈ Rn be independent centered random vectors with log-concave distribution and with the identity as covariance matrix.
WEAKENING ASSUMPTIONS FOR DETERMINISTIC SUBEXPONENTIAL TIME NON-SINGULAR MATRIX COMPLETION
WEAKENING ASSUMPTIONS DETERMINISTIC NON-SINGULAR MATRIX
2012/11/30
Kabanets and Impagliazzo [9] show how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial f...
Matrix Integrals and Several Integrable differential-difference Systems
Matrix integrals Pfa盿n, Casorati determinant two dimensional Toda lattice di甧rential-di甧rence KP equation semi-discrete Toda lattice
2012/8/1
In this paper, the relations between three special forms of matrix integrals and their associated integrable di甧rential-di甧rence systems are considered. It turns out that these matrix integrals with s...