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## Power Secant Method applied to natural frequency extraction of Timoshenko beam structures

Dias, Carlos Alberto Nunes
Fonte: LATIN AMER J SOLIDS STRUCTURES Publicador: LATIN AMER J SOLIDS STRUCTURES
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.18%
This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named ""power deflation"", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.

## On the generalized eigenvalue method for energies and matrix elements in lattice field theory

BLOSSIER, Benoit; MORTE, Michele Della; HIPPEL, Georg von; MENDES, Tereza; SOMMER, Rainer
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
35.98%
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

## Analise dinamica linear de porticos planos pelo metodo dos elementos finitos; Linear dynamic analysis of plane framework with use of the finite element method

Anderson Carlos Gatti
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
35.91%
Neste trabalho estuda-se o comportamento de pórticos planos submetidos a ações dinâmicas. Apresenta-se, inicialmente, a Equação de Movimento de Lagrange através das variações das energias cinética, potencial mais o trabalho das forças não conservativas. Em seguida, pelo emprego do Método dos Elementos Finitos são desenvolvidas as matrizes de rigidez, massa e amortecimento para o elemento de pórtico plano. O amortecimento introduzido é o de Rayleigh. Estudam-se dois métodos para a realização da análise dinâmica: o método de Newmark e o Método da Superposição Modal, também sendo realizado um estudo do problema de autovalor e autovetor pelo emprego do Método das Potências e o Método da Deflação de Wielandt. Os autovalores e autovetores fornecerão as freqüências naturais e os modos de vibração da estrutura. Finalmente, são mostrados exemplos numéricos para a análise do comportamento dos pórticos planos; In this work, it is studied the behavior of plane frames submitted to dynamic loads. First of all Lagrange?s Equations of Motion is presented by the kinetic and potential energy variation plus the work of the nonconservative forces. Next, the stiffness, mass and damping matrices for the plane frame element are developed with the use of the Finite Element Method. Damping is introduced from the Rayleigh damping. Both Newmark Method and Modal Superposition Method are studied to carry out the dynamic analysis. It is also carried out a study of the eigenvalue problem by Power Method and Wielandt Deflation Method. Eigenvalues and eigenvectors will provide the natural frequencies and normal modes of the structure...

## Análise de propagação de incertezas em método de estimação de rigidez estática por dados dinâmicos; Uncertainties propagation analysis through static stiffness estimation method from dynamic data

Robson Geremias Macedo
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
35.89%

## On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks

Zhang Yulin; Liu Zhongyun; Ferreira, Carla; Ralha, Rui
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.06%
We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.; Fundação para a Ciência e a Tecnologia (FCT)

## The first eigenvalue of the Laplacian and the Conductance of a Compact surface

Gracio, Clara; Ramos, José Sousa
Fonte: Nonlinear Dynamics Publicador: Nonlinear Dynamics
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.06%
We present some results with the central theme of is the phenomenon of the first eigenvalue of the Laplacian and conductance of the dynamical system. Our main tool is a method for studying how the hyperbolic metric on a Riemann surface behaves under deformation of the surface. With this model, we show variation of the first eigenvalue of the laplacian and the conductance of the dynamical system, with the Fenchel–Nielsen coordinates, that characterize the surface.

## Numerical resolution of cone-constrained eigenvalue problems

Pinto da Costa,A.; Seeger,Alberto
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
36.08%
Given a convex cone K and matrices A and B, one wishes to find a scalar λ and a nonzero vector x satisfying the complementarity system K ∋ x ⊥(Ax-λ Bx) ∈ K+. This problem arises in mechanics and in other areas of applied mathematics. Two numerical techniques for solving such kind of cone-constrained eigenvalue problem are discussed, namely, the Power Iteration Method and the Scaling and Projection Algorithm.

## Power secant method applied to natural frequency extraction of Timoshenko beam structures

Dias,C.A.N.
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
36.18%
This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named "power deflation", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.

## Blind channel identification and the eigenvalue problem of structured matrices

Ng, Michael K
Tipo: Working/Technical Paper Formato: 267487 bytes; 356 bytes; application/pdf; application/octet-stream
EN_AU
Relevância na Pesquisa
36.06%
In this paper, we address the problem of restoring a signal from its noisy convolutions with two unknown channels. When the transfer functions of these two channels have no common factors, the blind channel identification problem can be solved by finding the minimum eigenvalue of the Toeplitz-like matrix and its corresponding eigenvector. We present a fast iterative algorithm to solve the numerical solution of the eigenvalue problem for these structured matrices and hence the channel coeficients can be estimated efficiently. Once the channel coefficients are available, they can be used to reconstruct the unknown signal. Preliminary numerical results illustrate the effectiveness of the method.; no

## Numerical solution of the eigenvalue problem for Hermitian Toeplitz-like matrices

Ng, Michael K; Trench, William F
Tipo: Working/Technical Paper Formato: 247168 bytes; 356 bytes; application/pdf; application/octet-stream
EN_AU
Relevância na Pesquisa
36.23%
An iterative method based on displacement structure is proposed for computing eigenvalues and eigenvectors of a class of Hermitian Toeplitz-like matrices which includes matrices of the form T*T where T is arbitrary Toeplitz matrix, Toeplitz-block matrices and block-Toeplitz matrices. The method obtains a specific individual eigenvalue (i.e., the i-th smallest, where i is a specified integer in [1, 2,...,n]) of an n x n matrix at a computational cost of O(n2) operations. An associated eigenvector is obtained as a byproduct. The method is more efficient than general purpose methods such as the QR algorithm for obtaining a small number (compared to n) of eigenvalues. Moreover, since the computation of each eigenvalue is independent of the computation of all other eigenvalues, the method is highly parallelizable. Numerical results illustrate the effectiveness of the method.; no

## Meshless Eigenvalue analysis for resonant structures based on the radial point interpolation method

Kaufmann, T.; Fumeaux, C.; Engstrom, C.; Vahldieck, R.
Fonte: IEEE; USA Publicador: IEEE; USA
Tipo: Conference paper
Relevância na Pesquisa
36.02%
Meshless methods are a promising field of numerical methods recently introduced to computational electromagnetics. The potential of conformal and multi-scale modeling and the possibility of dynamic grid refinements are very attractive features that appear more naturally in meshless methods than in classical methods. The Radial Point Interpolation Method (RPIM) uses radial basis functions for the approximation of spatial derivatives. In this publication an eigenvalue solver is introduced for RPIM in electromagnetics. Eigenmodes are calculated on the example of a cylindrical resonant cavity. It is demonstrated that the computed resonance frequencies converge to the analytical values for increasingly fine spatial discretization. The computation of eigenmodes is an important tool to support research on a timedomain implementation of RPIM. It allows a characterization of the method’s accuracy and to investigate stability issues caused by the possible occurrence of non-physical solutions.; Thomas Kaufmann, Christophe Fumeaux, Christian Engstrom and Ruediger Vahldieck

## A stable cubically convergent GR algorithm and Krylov subspace methods for non-Hermitian matrix eigenvalue problems; A stable cubically convergent GR algorithm and Krylov subspace methods for non-Hermitian matrix eigenvalue problems; Ein stabiles kubisch konvergentes GR-Verfahren und Krylov-Verfahren für nichthermitesche Matrixeigenwertprobleme

Ziegler, Markus
Tipo: Dissertação
DE_DE
Relevância na Pesquisa
36.06%
In dieser Dissertation werden Krylov-Verfahren und Zerlegungsalgorithmen (GR-Algorithmen) zur Eigenwertberechnung von beliebigen Matrizen untersucht. Es wird gezeigt, dass das allgemeine restarted Krylov-Verfahren mathematisch äquivalent zum allgemeinen GR-Algorithmus ist. Ausgehend von diesem Ergebnis wird ein neues, numerisch stabiles GR-Verfahren entwickelt. Es wird bewiesen, dass dieses Verfahren, angewandt auf eine beliebig gegebene Matrix mit paarweise verschiedenen Eigenwerten, unter sehr schwachen Voraussetzungen kubisch konvergiert. Man beachte, dass das QR-Verfahren unter diesen Voraussetzungen i.a. nur quadratisch konvergiert.; In this thesis Krylov methods and algorithms of decomposition type (GR algorithms) for the eigenvalue computation of arbitrary matrices are discussed. It is shown that the general restarted Krylov method is mathematically equivalent to the general GR algorithm. Using this connection, a new, numerical stable GR algorithm is developed. It is proved that this algorithm converges cubically under mild conditions, when applied to any given matrix with distinct eigenvalues. Notice, that the QR algorithm converges typically quadratically under these conditions.

## Improving the Resolution of Bearing in Passive Sonar Arrays by Eigenvalue Analysis

Johnson, Don; DeGraaf, Stuart; Johnson, Don; DeGraaf, Stuart
Tipo: Relatório
ENG
Relevância na Pesquisa
36.18%
Tech Report; A method of improving the bearing-resolving capabilities of a passive array is discussed. This method is an adaptive beamforming method, having many similarities to the minimum energy approach. The evaluation of energy in each steered beam is preceded by an eigenvalue-eigenvector analysis of the emperical correlation matrix. Modification of the computations according to the eigenvalue structure result in improved resolution of the bearing of acoustic sources. The increase in resolution is related to the time-bandwidth product of the computation of the correlation matrix. However, this increased resolution is obtained at the expense of array gain.

## Computing matrix symmetrizers. Part 2: new methods using eigendata and linear means; a comparison

Martínez Dopico, Froilán C.; Uhlig, Frank
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article
Relevância na Pesquisa
35.86%
Over any field F every square matrix A can be factored into the product of two symmetric matrices as A = S1 . S2 with S_i = S_i^T ∈ F^(n,n) and either factor can be chosen nonsingular, as was discovered by Frobenius in 1910. Frobenius’ symmetric matrix factorization has been lying almost dormant for a century. The first successful method for computing matrix symmetrizers, i.e., symmetric matrices S such that SA is symmetric, was inspired by an iterative linear systems algorithm of Huang and Nong (2010) in 2013 [29, 30]. The resulting iterative algorithm has solved this computational problem over R and C, but at high computational cost. This paper develops and tests another linear equations solver, as well as eigen- and principal vector or Schur Normal Form based algorithms for solving the matrix symmetrizer problem numerically. Four new eigendata based algorithms use, respectively, SVD based principal vector chain constructions, Gram-Schmidt orthogonalization techniques, the Arnoldi method, or the Schur Normal Form of A in their formulations. They are helped by Datta’s 1973 method that symmetrizes unreduced Hessenberg matrices directly. The eigendata based methods work well and quickly for generic matrices A and create well conditioned matrix symmetrizers through eigenvector dyad accumulation. But all of the eigen based methods have differing deficiencies with matrices A that have ill-conditioned or complicated eigen structures with nontrivial Jordan normal forms. Our symmetrizer studies for matrices with ill-conditioned eigensystems lead to two open problems of matrix optimization.; This research was partially supported by the Ministerio de Economía y Competitividad of Spain through the research grant MTM2012-32542.

## The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.02%
In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are i

## An efficient method for computing eigenvalues of a real normal matrix

Zhou, B.B.; Brent, Richard
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.9%
Jacobi-based algorithms have attracted attention as they have a high degree of potential parallelism and may be more accurate than QR-based algorithms. In this paper we discuss how to design efficient Jacobi-like algorithms for eigenvalue decomposition of

## On the generalized eigenvalue method for energies and matrix elements in lattice field theory

Blossier, Benoit; Della Morte, Michele; von Hippel, Georg; Mendes, Tereza; Sommer, Rainer
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.98%
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as $\exp(-(E_{N+1}-E_n) t)$. The gap $E_{N+1}-E_n$ can be made large by increasing the number $N$ of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order $1/m_b$ in HQET.; Comment: (1+28) pages, 9 figures; minor corrections to table 1 and figures, main results unaffected

## Eigenvalue method to compute the largest relaxation time of disordered systems

Monthus, Cecile; Garel, Thomas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.18%
We consider the dynamics of finite-size disordered systems as defined by a master equation satisfying detailed balance. The master equation can be mapped onto a Schr\"odinger equation in configuration space, where the quantum Hamiltonian $H$ has the generic form of an Anderson localization tight-binding model. The largest relaxation time $t_{eq}$ governing the convergence towards Boltzmann equilibrium is determined by the lowest non-vanishing eigenvalue $E_1=1/t_{eq}$ of $H$ (the lowest eigenvalue being $E_0=0$). So the relaxation time $t_{eq}$ can be computed {\it without simulating the dynamics} by any eigenvalue method able to compute the first excited energy $E_1$. Here we use the 'conjugate gradient' method to determine $E_1$ in each disordered sample and present numerical results on the statistics of the relaxation time $t_{eq}$ over the disordered samples of a given size for two models : (i) for the random walk in a self-affine potential of Hurst exponent $H$ on a two-dimensional square of size $L \times L$, we find the activated scaling $\ln t_{eq}(L) \sim L^{\psi}$ with $\psi=H$ as expected; (ii) for the dynamics of the Sherrington-Kirkpatrick spin-glass model of $N$ spins, we find the growth $\ln t_{eq}(N) \sim N^{\psi}$ with $\psi=1/3$ in agreement with most previous Monte-Carlo measures. In addition...

## Complex-band-structure eigenvalue method adapted to Floquet systems: topological superconducting wires as a case study

Reynoso, Andres A.; Frustaglia, Diego