Perturbation of Higher-Order Singular Values

Perturbation of higher-order singular values

The higher-order singular values for a tensor of order d are defined as the singular values of the d different matricizations associated with the multilinear rank. When d ≥ 3, the singular values are generally different for different matricizations but not completely independent. Characterizing the set of feasible singular values turns out to be difficult. In this work, we contribute to this qu...

Reduction of Singular Lagrangians of Higher-order

Given a singular non-autonomous Lagrangian of higher order we construct a reduced evolution space of the same order and a local regular Lagrangian on it which is gauge equivalent to the original one. The general geometrical framework used is the theory of almost stable tangent geometry of higher order introduced in 17]. We show that higher order almost stable manifols can be endowed with a loca...

Singular Sets of Higher Order Elliptic Equations

The implicit function theorem implies that the zero set of a smooth function, the set where the function vanishes, is a smooth hypersurface away from the critical zero set. Hence to study zero sets it is important to understand the structure of the critical zero sets. For solutions of the second order elliptic equations the critical zero sets represent the singular parts of zero sets. They have...

Perturbation bounds for eigenvalues of diagonalizable matrices and singular values

INVESTIGATION OF BOUNDARY LAYERS IN A SINGULAR PERTURBATION PROBLEM INCLUDING A 4TH ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.