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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 ...
William C. Taylor, Palmer R. Schlegel
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Computation of an eigenvector of a symmetric tridiagonal matrix
Siberian Mathematical Journal, 1985A new algorithm for the computation of an eigenvector of a symmetric tridiagonal matrix is given with error estimation. This estimation depends only on the order of numbers in the computer.
Godunov, S. K. +2 more
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A Note on a Three-Term Recurrence for a Tridiagonal Matrix
Applied Mathematics and Computation, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Moawwad El-Mikkawy
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Bounds for entries of the inverse matrix of a tridiagonal matrix
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the inverse of a quasi-tridiagonal matrix
International Journal of Computer Mathematics, 1986Explicit relations are derived between the elements of the inverse of a quasi-tridiagonal matrix and the elements of the inverse of the associated tridiagonal matrix. These relations are used to compute the quasi-tridiagonal inverse assuming that the tridiagonal inverse is known.
W. M. Pickering, M. J. Piff
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Fibonacci Polynomials and Sylvester Determinant of Tridiagonal Matrix
Applied Mathematics and Computation, 2010Consider the \((n+1)\times(n+1)\) tridiagonal matrix \(M_{n}(x,y)\) with diagonal \(x,x+y,\dots,x+ny\), subdiagonal \(n,n-1,\dots,1\) and superdiagonal \(1,2,\dots,n\). The author proves that the eigenvalues of \(M_{n}(0,y)\) are \(\frac{1}{2}ny+\frac {1}{2}(n-2k)\sqrt{4+y^{2}}\) for \(k=0,1,\dots,n\) and hence that \(\det M_{n}(x,y)\) equals ...
Wenchang Chu
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A system of equations with a tridiagonal coefficient matrix
Applied Mathematics and Computation, 2004The goal of the paper is to show that for a linear system of equations \(AX=C\), where the coefficient matrix \(A\) is tridiagonal, the algorithms used by \textit{M. El-Mikkawy} in [Appl. Math. Comput. 139, No. 2--3, 503--511 (2003; Zbl 1078.65533)] can be improved in the case when \(A\) is invertible, the system being equivalent with a linear system ...
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Calculation of the Eigenvalues of a Tridiagonal Hermitian Matrix
Journal of Mathematical Physics, 1961For real symmetric or Hermitian matrices with tridiagonal form, the secular equation may be written as a continued fraction equation f(λ)=0. f(λ) is a member of a recursively defined sequence R(n)(λ) of n continued fractions if the secular equation is of the nth order. The basis for a new method of computing the eigenvalues of such tridiagonal matrices
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An explicit inverse of a tridiagonal matrix
International Journal of Computer Mathematics, 1983An explicit expression for the inverse of an invertible, real tridiagonal matrix is obtained, and its principal structural properties are determined. An efficient and stable algorithm is developed by utilising these properties.
S.R. Vatsya, H.O Pritchard
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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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