We use the QR-decomposition to obtain the eigenvalues of a matrix. The method is iterative and builds an upper-triangular matrix. The eigenvalues appear as the diagonal terms of this upper-triangular matrix. These values are found to be in agreement with those given by the Mathematica built-...
Quantum matrix algebras of the GL(m|n) type: The structure and spectral parameterization of the characteristic subalgebra We continue the study of quantum matrix algebras of the GL ( m|n ) type. We find three alternative forms of the Cayley-Hamilton identity; most importantly,... DI Gurevich...
Asymptotic behavior of the self-defocusing nonlinear Schrödinger equation for piecewise constant initial conditions In this paper we use a transfer matrix method to calculate the asymptotic behavior of the nonlinear Schr枚dinger (NLS) equation in a self-defocusing medium... PB Lundquist,DR Andersen...
摘要: Autovectors The term "eigenvalues" refers to the variance of a data matrix. While a common term in matrix algebra, in statistics, eigenvalues are commonly discussed in factor analysis. Here, an...关键词:中国 信息技术 软件产业 国际化 ...
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space #36;l^2(#92;mathbb{N})#36; by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator...
Krause, “Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix,” Linear Algebra and Its Applications, vol. 142, pp. 195–209, 1990. CrossRef N. Gozlan, “A characterization of dimension free concentration in terms of transportation inequalities,” The ...
matrix) + "}" stiffness_matrix_str = numpy_to_mathematica(stiffness_matrix) mass_matrix_str = numpy_to_mathematica(mass_matrix) # Start a Wolfram Language session session = WolframLanguageSession() # Wolfram code to calculate eigenvalues and eigenvectors wolfram_code = f""" stiffnessMatrix = ...
diagonal entry equal to zero. We shall denote the characteristic polynomial of G by P(x, G) = det(xI −A(G)) = n i=0 a i x n−i . Since A(G) is a real symmetric matrix, its eigenvalues, say λ i (A(G))(i = 1, 2, ··· , n), are real numbers, and may be...
In this paper, we first derive a family of iterative schemes with fourth order. A weight function is used to maintain its optimality. Then, we transform it into methods with several self-accelerating parameters to reach the highest possible convergence r
A perturbation method for weakly damped systems repeated eigenvalues; 具有重特征值的弱阻尼系统的摄动法 3. This paper points out that even if under assumption of symmetric matrix ψ1,MoZo for the repeated eigenvalue,the solution of sensitivity equation contained μ is independent of μ. 本文指出...