Linearization method in classification problems of linear algebra
نویسنده
چکیده
The author devised in [Math. USSR–Izv. 31 (1988) 481– 501] a procedure that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. We give a brief exposition of this method, review results that were obtained by using this method (and were published mainly in Russian), and give examples of classification problems that can be solved by this method.
منابع مشابه
Free Vibration Analysis of Quintic Nonlinear Beams using Equivalent Linearization Method with a Weighted Averaging
In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, whic...
متن کاملA short course on exponential integrators
This paper contains a short course on the construction, analysis , and implementation of exponential integrators for time dependent partial differential equations. A much more detailed recent review can be found in Hochbruck and Ostermann (2010). Here, we restrict ourselves to one-step methods for autonomous problems. A basic principle for the construction of exponential integra-tors is the lin...
متن کاملModified Linear Approximation for Assessment of Rigid Block Dynamics
This study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. Linearization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...
متن کاملA New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
متن کاملA linearization of PDEs based on conservation laws
A method based on innnite parameter conservation laws is described to factor linear differential operators out of nonlinear partial diierential equations (PDEs) or out of diierential consequences of nonlinear PDEs. This includes a complete linearization to an equivalent linear PDE (system) if that is possible. Innnite parameter conservation laws can be computed, for example, with a computer alg...
متن کامل