Efficient algorithm for solving tridiagonal quasi-Toeplitz linear systems
25 Nov 2022
TL;DR: In this article , a fast algorithm for solving the special tridiagonal quasi-toeplitz system is presented where the bandwidth of a quasi-Toeplit is larger than the one of Toeplite.
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Abstract: Abstract In this paper, a fast algorithm for solving the special tridiagonal quasi-Toeplitz system is presented where the bandwidth of a quasi-Toeplitz is larger than the one of Toeplitz. Our algorithm is quite competitive with the classic LU method. Some examples demonstrate the good efficiency and stability of our algorithm.
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References
Tridiagonal Toeplitz matrices: properties and novel applications
TL;DR: The eigenvalues and eigenvectors of tridiagonal Toeplitz matrices are known in closed form and explicit expressions for the structured distance to the closest normal matrix, the departure from normality, and the ϵ-pseudospectrum are derived.
A fast algorithm for solving special tridiagonal systems
Wen-Ming Yan,Kuo-Liang Chung +1 more
TL;DR: A fast algorithm for solving the special tridiagonal system, a symmetric diagonally dominant and Toeplitz system of linear equations, which is quite competitive with the Gaussian elimination, cyclic reduction, specialLU factorization, reversed triangular factorizations, and ToEplitz factorization methods.
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A fast method for solving a class of tridiagonal linear systems
TL;DR: It is proved that the diagonals of theLU decomposition of the coefficient matrix rapidly converge to full floating-point precision, and that the limits of the LU diagonal limits are roughly within machine precision of the limits using real arithmetic.
38
Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes
TL;DR: The class of quasi-Toeplitz matrices is a Banach algebra with a suitable sub-multiplicative matrix norm as discussed by the authors, and the class of CQT matrices can be expressed as a quasi-Banach algebra.
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On the exponential of semi-infinite quasi-Toeplitz matrices
Dario Andrea Bini,Beatrice Meini +1 more
TL;DR: It is proved that the exponential of a QT-matrix A is QT, that is,exp (A) = T(\exp (a))+F$$exp(A)=T(exp(a)+F where F is a compact operator in $$\ell ^p$$ℓp.
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