First order sensitivity analysis of symplectic eigenvalues
نویسندگان
چکیده
منابع مشابه
First-order optical systems with unimodular eigenvalues.
It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. More...
متن کاملSecond order sensitivity analysis for shape optimization of continuum structures
This study focuses on the optimization of the plane structure. Sequential quadratic programming (SQP) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. A new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. All the second order required derivatives will be calculat...
متن کاملShape Sensitivity Analysis of Eigenvalues Revisited
A. The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As a result, the asymptotic expansions of eigenvalues are obtained and discussed in terms of integral attributes of the geometrical perturbations including the virtual mass tensor, polarizati...
متن کاملOn the sensitivity analysis of eigenvalues
Let λ be a simple eigenvalue of an n-by-n matrix A. Let y and x be left and right eigenvectors of A corresponding to λ, respectively. Then, for the spectral norm, the condition number cond(λ,A) := ‖x‖2 ‖y‖2/|yx| measures the sensitivity of λ to small perturbations in A and plays an important role in the accuracy assessment of computed eigenvalues. R. A. Smith [Numer. Math., 10(1967), pp.232-240...
متن کاملAccurate First-Order Sensitivity Analysis for Delay Differential Equations
In this paper, we derive an equation governing the dynamics of firstorder forward sensitivities for a general system of parametric neutral delay differential equations (NDDEs). We also derive a formula which identifies the size of jumps that appear at discontinuity points when the sensitivity equations are integrated. The formula leads to an algorithm which can compute sensitivities for various...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2020
ISSN: 0024-3795
DOI: 10.1016/j.laa.2020.07.003