Low-rank approximation with zeros aims to find a matrix of fixed rank and zero pattern that minimizes the Euclidean distance given data matrix. We study critical points this optimization problem using algebraic tools. In particular, we describe special linear, affine, determinantal relations satisfied by points. also investigate number how is related complexity nonnegative factorization problem.

We propose a fast method of high order approximations for the solution stationary thermoelastic system in ℝ3 unknown displacement vector u and temperature T. The problem determining T is an independent can be obtained by solving Dirichlet Laplace equation. When known, Lamé system, where gradient treated as mass force. Using basis functions introduced theory approximate approximations, we derive...

Abstract We develop an asymptotic expansion for small time of the density solution a non-degenerate system stochastic differential equations with smooth coefficients, and apply this to stepwise approximation solutions. The expansion, which takes form multivariate Edgeworth-type is obtained from Kolmogorov forward equation using some standard PDE results. To generate one step solution, we use Co...