Journal Article10.1007/S10483-009-0212-X
An inversion algorithm for general tridiagonal matrix
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TL;DR: In this article, an algorithm for the inverse of a general tridiagonal matrix is presented, which is then generalized to deal with general tridagonal matrices without any restriction, indicating low computational complexity of the proposed algorithm.
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Abstract: An 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. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.
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Citations
A new recursive algorithm for inverting general k-tridiagonal matrices
Moawwad El-Mikkawy,Faiz Atlan +1 more
TL;DR: A new breakdown-free recursive algorithm for inverting general k -tridiagonal matrices without imposing any simplifying assumptions is given.
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Explicit inverse of tridiagonal matrix with applications in autoregressive modelling
TL;DR: In this paper, the inverse of a class of symmetric tridiagonal matrices, which is almost Toeplitz, except that the first and last diagonal elements are different from the rest, is presented.
A novel algorithm for inverting a general k-tridiagonal matrix
Moawwad El-Mikkawy,Faiz Atlan +1 more
TL;DR: A novel algorithm, that will never fail, for inverting a general nonsingular k -tridiagonal matrix is presented and the computational cost is given.
18
On an inverse formula of a tridiagonal matrix
TL;DR: In this article, an alternative version of the Usmani formula for tridiagonal matrices has been proposed, which can be obtained by a simple transformation of the Meamani formula.
Majorization–Minimization approach for real-time enhancement of sparsity-driven SAR imaging
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References
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On the inverse of a general tridiagonal matrix
TL;DR: A new efficient computational algorithm to find the inverse of a general tridiagonal matrix is presented and is suited for implementation using computer algebra systems such as MAPLE, MATHEMATICA, MATLAB and MACSYMA.
Decay Rates of the Inverse of Nonsymmetric Tridiagonal and Band Matrices
TL;DR: This work characterize certain properties of A, i.e., being an M-matrix or positive definite, in terms of the ui, vi,xi, and yi, and establishes a relation of zero row sums and zero column sums of A and pairwise constant ui.
A review on the inverse of symmetric tridiagonal and block tridiagonal matrices
TL;DR: Results are obtained by relating the elements of inverses to elements of the Cholesky decompositions of these matrices, which gives explicit formulas for the element of the inverse and gives rise to stable algorithms to compute them.
The inverse of a tridiagonal matrix
TL;DR: In this paper, explicit formulae for the elements of the inverse of a general tridiagonal matrix are presented by first extending results on the explicit solution of a second-order linear homogeneous difference equation with variable coefficients to the nonhomogeneous case, and then applying these extended results to a boundary value problem.