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On the powers and the inverse of a tridiagonal matrix
Applied Mathematics and Computation, 2009In this paper, we present an eigendecomposition of a tridiagonal matrix. Tridiagonal matrix powers and inverse are derived. As consequence, we get some relations verified by the coefficients of the inverse and the powers of a tridiagonal matrix.
Mohamed Elouafi, Ahmed Driss Aiat Hadj
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The Inverse of a Tridiagonal Matrix
1972Abstract : The closed form inverse of a fairly general tridiagonal matrix is given. The restriction is that the off-diagonal elements in the tridiagonal band be nonzero. If the elements of the matrix are integers, where the upper off-diagonal elements are equal and the lower off-diagonal elements are equal, then an integer multiple of each element of ...
Palmer R. Schlegel, William C. Taylor
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Tridiagonalization of a symetric band matrix
Numerische Mathematik, 1968The well known method proposed by Givens [1] reduces a full symmetric matrix A = (a ik ) of order n by a sequence of appropriately chosen elementary orthogonal transformations (in the following called Jacobi rotations) to triput diagonal form. This is achieved by (n - 1)(n - 2)/2 Jacobi rotations, each of which annihilates one of the elements a ik with
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On a conjecture about a tridiagonal matrix
Journal of Information and Optimization Sciences, 2020In this note we answer to a recent conjecture posed by Q.M. Al-Hassan on a factorization for the characteristic polynomial of the tridiagonal matrix with zero main diagonal and all 1’s sub- and sup...
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Eigenvalue problem for an infinite tridiagonal matrix
Journal of Mathematical Physics, 1981A method is developed for the calculation of the eigenvectors of an infinite tridiagonal matrix. Possible application of this method to study the problem of localization in a disordered linear chain is also discussed.
S. Y. Wu, C. C. Shih, C. Wongtawatnugool
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On the inverse of a general tridiagonal matrix
Applied Mathematics and Computation, 2004In the current paper a new efficient computational algorithm to find the inverse of a general tridiagonal matrix is presented. The algorithm is suited for implementation using computer algebra systems such as MAPLE, MATHEMATICA, MATLAB and MACSYMA. Symbolic and numeric examples are given.
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An algorithm for the numerical inversion of a tridiagonal matrix [PDF]
Communications in Numerical Methods in Engineering, 1993 AbstractThis paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient.
Árpád Pethö, Shashi, Surendra Kumar
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On the factorization and the inverse of a tridiagonal matrix [PDF]
Journal of Discrete Mathematical Sciences and Cryptography, 2021 Boutaina Talibi +2 more
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Perturbation of a Tridiagonal Stability Matrix
Mathematics Magazine, 1994(1994). Perturbation of a Tridiagonal Stability Matrix. Mathematics Magazine: Vol. 67, No. 2, pp. 124-127.
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An inversion algorithm for general tridiagonal matrix
Applied Mathematics and Mechanics, 2009An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction.
Rui-sheng Ran +3 more
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