Results 21 to 30 of about 1,655,330 (212)
On the Computation of the Eigenvalues of a Tridiagonal Matrix [PDF]
Mathematics of Computation, 1969 A recent algorithm for the simultaneous approximation of all zeros of a polynomial is applied to the computation of the eigenvalues of a tridiagonal matrix. The method works in the presence of multiplicity and degeneracy and has been tested in a multitude of cases ; its practical limitation on a computer is the large number of locations required for ...
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A deflation formula for tridiagonal matrices [PDF]
, 1980 summary:An explicit formula for the deflation of a tridiagonal matrix is presented.
Fiedler, Miroslav
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The interesting spectral interlacing property for a certain tridiagonal matrix [PDF]
, 2020 In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a principal submatrix is also of a Sylvester-Kac matrix ...
Kılıç, Emrah +2 more
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State-Space Parametrizations of Multivariable Linear Systems using Tridiagonal Matrix Forms
, 1996 Tridiagonal parametrizations of linear state-space models are proposed for multivariable system identification. The parametrizations are surjective, i.e. all systems up to a given order can be described.
Helmersson, Anders,, McKelvey, Tomas,
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Computing the eigenvalues and eigenvectors of a general matrix by reduction to general tridiagonal form [PDF]
, 1990 This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, compute the eigenvalues of the tridiagonal matrix, improve the accuracy of an eigenvalue, and compute the corresponding eigenvector.
Geist, G. A. +2 more
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A new approach to tridiagonal matrices related to the Sylvester–Kac matrix [PDF]
Notes on Number Theory and Discrete MathematicsThe Sylvester–Kac matrix, a well-known tridiagonal matrix, has been extensively studied for over a century, with various generalizations explored in the literature.
Efruz Özlem Mersin, Mustafa Bahşi
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VanderLaan Circulant Type Matrices
Abstract and Applied Analysis, 2015 Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices.
Hongyan Pan, Zhaolin Jiang
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Explicit inverse of a tridiagonal k−Toeplitz matrix [PDF]
Numerische Mathematik, 2005 The paper presents explicit expressions for the entries of the inverse of a tridiagonal \(k\)-Toeplitz matrix \(A\). Conditions for the existence of \(A^{-1}\) are obtained from an explicit expression of the characteristic polynomial of \(A\). The results presented in the paper extend known results for the case when the residue \(\operatorname {mod} k\)
Fonseca, C. M. da, Petronilho, J.
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ANALYTICAL INVERSE FOR THE SYMMETRIC CIRCULANT TRIDIAGONAL MATRIX [PDF]
Far East Journal of Applied Mathematics, 2018 Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce the matrix to a simple form, only then beginning a mathematical procedure.
Seyyed Mostafa Mousavi Janbeh Sarayi +3 more
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Remark on the eigenvalues of a tridiagonal matrix in biogeography
Applied Mathematics and Computation, 2023 The main result proved in [The eigenvalues of a tridiagonal matrix in biogeography, Appl. Math. Comput. 218 (2011) 195-201; MR2821464] by B. Igelnik and D. Simon is virtually the Sylvester determinant.
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