Eigenvalue Sensitivity Analysis for a Combined Beam Structure with Varying Constraints

II. Eigenvalue Sensitivity Analysis

Sensitivity analysis for the multivariate eigenvalue problem

This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds...

Subspace identification with eigenvalue constraints

Standard subspace methods for the identification of discrete-time, linear, time-invariant systems are transformed into generalized convex optimization problems in which the poles of the system estimate are constrained to lie within user-defined convex regions of the complex plane. The transformation is done by restating subspace methods such as the minimization of a Frobenius norm affine in the...

A Support Function Based Algorithm for Optimization with Eigenvalue Constraints

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because of a wide range of applications in fields such as structural design and control theory. Here we focus on the optimization of a linear objective subject to a constraint on the smallest eigenvalue of an analytic and...

Perturbation Theory Eigenvalue Sensitivity Analysis with Monte Carlo Techniques

Methodologies to calculate adjoint-based first-order-linear perturbation theory sensitivity coefficients with multigroup Monte Carlo methods are developed, implemented, and tested in this paper. These techniques can quickly produce sensitivity coefficients for all nuclides and reaction types for each region of a system model. Monte Carlo techniques have been developed to calculate the neutron f...