Journal ArticleDOI
Random matrix eigenvalue problems in structural dynamics: An iterative approach
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TLDR
Computationally efficient methods for random eigenvalue problems arising in the dynamics of multi-degree-of-freedom systems are developed using a Galerkin formulation to obtain the unknown coefficients.About:
This article is published in Mechanical Systems and Signal Processing.The article was published on 2022-02-01. It has received 3 citations till now. The article focuses on the topics: Eigenvalues and eigenvectors & Eigenvalues and eigenvectors.read more
Citations
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An efficient reduced‐order method for stochastic eigenvalue analysis
TL;DR: In this paper , the authors presented an efficient numerical algorithm to compute eigenvalues of stochastic problems with low computational effort, which avoids the curse of dimensionality with great success.
Journal ArticleDOI
About the method of assessing the quality of big technical systems based on the rules of subtraction of matrices of values of indicators
K.Z. Bilyatdinov,E.A. Krivchun +1 more
TL;DR: In this article , the authors present a basic formula and a universal table for the development of structure functional models of big technical systems, which takes into account priorities of performed functions and substructures, also, maximum and minimum values of basic indices of technical systems.
Numerical Solution of Free Stochastic Differential Equations
TL;DR: In this article , a free analog of the Euler-Maruyama method (fEMM) was derived to numerically approximate solutions of free stochastic differential equations (fSDEs).
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Book
Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
Journal ArticleDOI
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.
Journal ArticleDOI
Rates of change of eigenvalues and eigenvectors.
R. L. Fox,M. P. Kapoor +1 more
TL;DR: Exact expressions for rates of change of eigenvalues and eigenvector to facilitate computerized design of complex structures are presented.