We prove new results about the robustness of well-known convex noise-blind optimization formulations for reconstruction low-rank matrices from an underdetermined system random linear measurements. Specifically, our address Hermitian rank-one measurements as used in a version phase retrieval problem; that is, each measurement can be represented inner product unknown matrix and outer given realiz...

Let E be an optimal elliptic curve of conductor N , such that the L-function of E vanishes to order one at s = 1. Let K be a quadratic imaginary field in which all the primes dividing N split and such that the L-function of E over K also vanishes to order one at s = 1. In view of the Gross-Zagier theorem, the second part of the Birch and Swinnerton-Dyer conjecture says that the index in E(K) of...

Low-rank matrix recovery is an active topic drawing the attention of many researchers. It addresses the problem of approximating the observed data matrix by an unknown low-rank matrix. Suppose that A is a low-rank matrix approximation of D, where D and A are [Formula: see text] matrices. Based on a useful decomposition of [Formula: see text], for the unitarily invariant norm [Formula: see text]...

We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix. This one customary approach to build recommender systems. give algorithm for computing associated condition number and demonstrate experimentally how measurements ...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...