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How many random entries of an n × nα, rank r matrix are necessary to reconstruct the matrix within an accuracy δ? We address this question in the case of a random matrix with bounded rank, whereby the...
We consider the problem of learning a coecient vector x0 2 R N from noisy linear observation y = Ax0 + w 2 R n. In many contexts (ranging from model selection to image processing) it is desirable to ...
In this paper we show how the transformations associated with the reduction to the Smith form of some classes of multivariate polynomial matrices are computed. Using a Maple implementation of a constr...
Abstract: In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous determini...
For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence D-NAN is investigated. As a special case, necessary and sufficient conditions are given for the convergence of...
Consider a deterministic self-adjoint matrix Xn with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limit...
A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear eq...
Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement ra...
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of practical and ecient structured preconditioners through matrix transformation and matrix approxima...

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