Left-eigenvectors are certificates of the Orbit Problem
نویسندگان
چکیده
This paper investigates the connexion between the Kannan-Lipton Orbit Problem and the polynomial invariant generator algorithm PILA based on eigenvectors computation. Namely, we reduce the problem of generating linear and polynomial certificates of non-reachability for the Orbit Problem for linear transformations with coefficients in Q to the generalized eigenvector problem. Also, we prove the existence of such certificates for any transformation with integer coefficients, which is not the case with rational coefficients. 1998 ACM Subject Classification F.3.1, D.2.4
منابع مشابه
A Rare Penetrating Trauma of Both Orbit and Nasal Cavity
Introduction: Diagnosis of orbital foreign body (FB) penetration is usually obvious when part of the FB is still attached at the entry wound (1). However, the depth and course of the FB in this case was not visible. Case Report: A 5-year old female presented with a pencil penetrating the left orbit. A computed tomography (CT) scan showed that the pencil penetrated the left orbit (extraseptal)...
متن کاملEfficient Optimum Design of Steructures With Reqency Response Consteraint Using High Quality Approximation
An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main ideals to reduce the number of dynamic analysis by introducing high quality approximation. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A tw...
متن کاملLow-Thrust Optimal Orbit Raising with Plane Change
A new guidance scheme for the problem of Low-thrust transfer between inclined orbits is developed within the framework of optimal control theory. The objective of the guidance scheme is to provide the appropriate thrust steering program that will transfer the vehicle from an inclined low earth orbits to the high earth orbits. The presented guidance scheme is determined using Pontryagin’s princi...
متن کاملUsing the eigenvalues of the sound equation to determine the properties of materials
In this article, the eigenvalues of the sound equation are used to determine the refractive index. This refractive index helps to extract the acoustic components of the material such as the speed of sound in the material. This will help in identifying targets, especially in the field of signal processing. For this purpose, a method has been extracted that can be used to establish a relation bet...
متن کاملHigh Accuracy Relative Motion of Spacecraft Using Linearized Time-Varying J2-Perturbed Terms
This paper presents a set of linearized equations was derived for the motion, relative to an elliptical reference orbit, of an object influenced by J2 perturbation terms. Approximate solution for simulations was used to compare these equations and the linearized keplerian equations to the exact equations. The inclusion of the linearized perturbations in the derived equations increased the high ...
متن کامل