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On the explicit inverse and conditioning of a tridiagonal matrix
International Journal of Computer Mathematics, 1992The expressions for the elements of the inverse of the tridiagonal matrix P n (x y) = [P ij ] so that P ii = 1P i. i+1 = − y, P i+1,i = −x, are obtained. Employing these expressions, we compute which is required in proving that the matrix P n (x y) is well-conditioned if x ≥ 0, y ≥ 0, x + y ≤ 1. Similar results are obtained for some related tridiagonal
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Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix
SIAM Journal on Matrix Analysis and Applications, 2006In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n‐step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure.
Holger Dette +3 more
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𝑞-Deformation of the Kac-Sylvester tridiagonal matrix
Proceedings of the American Mathematical Society, 2021Upon replacing integers by q q -integers, one arrives at a natural
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Tridiagonalization of a Symmetric Dense Matrix on a GPU Cluster
2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum, 2013Symmetric dense Eigen value problems arise in many scientific and engineering simulations. In this paper, we use GPUs to accelerate its main computational kernel, the tridiagonalization of a dense symmetric matrix on a distributed multicore architecture.
Ichitaro Yamazaki +3 more
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Algorithm for solving tridiagonal matrix problems in parallel
Parallel Computing, 1995Abstract A new algorithm is presented, designed to solve tridiagonal matrix problems efficiently with parallel computers (multiple instruction stream, multiple data stream (MIMD) machines with distributed memory). The algorithm is designed to be extendable to higher order banded diagonal systems.
Nathan Mattor +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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Fibonacci identities via the determinant of tridiagonal matrix
Applied Mathematics and Computation, 2011Let \(F_n\) be the Fibonacci numbers. The author proves the identity \[ F_{m+n+1}=F_{m+1}F_{n+1}+F_m F_n \] using determinants of tridiagonal matrices.
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Reconstruction of a tridiagonal matrix
Two algorithms are given for the task of reconstructing certain symmetric tri-diagonal Jacobi matrices, needed in connection with orthogonal polynomials. Both algorithms are based on a factorization of the Vandermonde matrix, and both necessitate the solution of a sequence of linear systems of increasing order, which may be accomplished through a ...Koshcheeva, I. V., Kuznetsov, Yu. I.
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On the factorization and the inverse of a tridiagonal matrix
Journal of Discrete Mathematical Sciences and Cryptography, 2021Boutaina Talibi +2 more
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