Nonnegativity Preservation under Singular Values Perturbation

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...

Singular Vector Perturbation Under Gaussian Noise

We perform a non-asymptotic analysis on the singular vector distribution under Gaussian noise. In particular, we provide sufficient conditions on a matrix for its first few singular vectors to have near normal distribution. Our result can be used to facilitate the error analysis in linear dimension reduction.

Perturbation bounds for eigenvalues of diagonalizable matrices and singular values

Invariance of Total Nonnegativity of a Tridiagonal Matrix Under Element-Wise Perturbation

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Persistent Homoclinic Orbits for Nonlinear Schrödinger Equation Under Singular Perturbation

Existence of homoclinic orbits in the cubic nonlinear Schrödinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup eǫt∂ 2 x at ǫ = 0. This article is a substantial generalization of [3], and motivated by the effort of Dr. Zeng [9] [8]. The mistake of Zeng in [8] is corrected with a normal form transform approach. Both one and two unstable ...