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A kind of inverse eigenvalue problems of Jacobi matrix
Applied Mathematics and Computation, 2006The authors consider the problem of reconstructing two \(n\times n\) Jacobi matrices \(J_{n},\;J_{n}^{\ast }\) and vectors \(X_{1}\), \(Y_{1}\in \mathbb{R}^{k}\) such that for a given \(k\times k\) Jacobi matrix \(J_{k}\) where \( \left( 1\leq k\leq n-1\right) \), real scalars \(S,\; \lambda,\; \mu \) and vectors \(X_{2},\) \(Y_{2}\in \mathbb{R}^{n-k}\)
Juan Peng, Xi-Yan Hu, Lei Zhang 0010
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1994
Abstract Characteristic properties of natural systems can often be described by eigenvalues of certain differential equations, see Chapter 8. If the differential equation is discretized, a matrix eigenvalue problem has to be solved. This kind of problem will be considered in this chapter. We will restrict ourselves to real matrices.
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Abstract Characteristic properties of natural systems can often be described by eigenvalues of certain differential equations, see Chapter 8. If the differential equation is discretized, a matrix eigenvalue problem has to be solved. This kind of problem will be considered in this chapter. We will restrict ourselves to real matrices.
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2008
This chapter explains the eigenvalue problem or the determination of the eigenvalues and eigenvectors of a square matrix, which is important in many branches of the physical sciences and engineering. The chapter discusses the properties of eigenvalues and eigenvectors.
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This chapter explains the eigenvalue problem or the determination of the eigenvalues and eigenvectors of a square matrix, which is important in many branches of the physical sciences and engineering. The chapter discusses the properties of eigenvalues and eigenvectors.
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2000
Abstract Where I is the uni matrix. This is the characteristic equation of the matrix A. If we expand the determinant by Cramer’s rule (cf chapter 10) we see that pA is a polynomial of degree n in λ. The characteristic equation therefore possesses n roots λi, not all necessarily distinct from each other, which are the eigenvalues of ...
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Abstract Where I is the uni matrix. This is the characteristic equation of the matrix A. If we expand the determinant by Cramer’s rule (cf chapter 10) we see that pA is a polynomial of degree n in λ. The characteristic equation therefore possesses n roots λi, not all necessarily distinct from each other, which are the eigenvalues of ...
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2014
The eigenvalues and eigenvectors of a matrix play an important role in many settings in physics and engineering.
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The eigenvalues and eigenvectors of a matrix play an important role in many settings in physics and engineering.
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Eigenvalue problem for an irregular ?-matrix
Journal of Soviet Mathematics, 1980The solution of the eigenvalue problem is examined for the polynomial matrixD(λ)=Aoλs+A1λs−1+...+As when the matricesA0 andA2 (or one of them) are singular. A normalized process is used for solving the problem, permitting the determination of linearly independent eigenvectors corresponding to the zero eigenvalue of matrixD(λ) and to the zero eigenvalue
V. N. Kublanovskaya +2 more
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1998
Many problems in science and engineering lead to eigenvalue problems for matrices. These occur either directly or by discretization of eigenvalue problems for differential or integral operators. In the latter case the size of the matrices will be rather large.
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Many problems in science and engineering lead to eigenvalue problems for matrices. These occur either directly or by discretization of eigenvalue problems for differential or integral operators. In the latter case the size of the matrices will be rather large.
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Numerical validation for an inverse matrix eigenvalue problem
Computing, 1994The authors consider the following problem (called the additive inverse eigenvalue problem): Given \(n + 1\) real symmetric \(n \times n\) matrices \(A_ i\), \(i = 0, 1, \dots, n\), and given \(n\) real numbers \(\lambda_ 1 < \lambda_ 2 < \dots < \lambda_ n\), prove that there are \(n\) real numbers \(c^*_ i\), \(i = 1, \dots, n\), such that the matrix
Götz Alefeld, A. Gienger, Günter Mayer
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On matrix inverse eigenvalue problems
Inverse Problems, 1998Results are presented regarding the inverse problem for a multiparameter perturbed linear operator on \(\mathbb{C}^n\). [Cf. \textit{F. V. Atkinson}, Multiparameter eigenvalue problems. Volume I: Matrices and compact operators. (1972; Zbl 0555.47001).] Given an \((n,n)\) matrix (i) \(A(t_1,\dots, t_n)= C_0+ \sum^n_{i=1} t_iC_i\) with eigenvalues ...
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The Solution of Matrix Eigenvalue Problems
1978Let A be a square matrix of order n. Consider the equation $$Ax = \,\lambda x,$$ (7.1) where λ is a real or complex number and x is an n-tuple. For x = 0, equation (7.1) is satisfied by an arbitrary scalar λ. The values of λ for which there exists some nonzero vector x satisfying (7.1) are called eigenvalues and the corresponding vectors x ...
Ferenc Szidarovszky, Sidney Yakowitz
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