A symbolic algorithm for periodic tridiagonal systems of equations

DOI10.1007/S10910-014-0378-1zbMath1300.65014OpenAlexW2038366383MaRDI QIDQ460971

Qiong-Xiang Kong, Ji-Teng Jia

Publication date: 9 October 2014

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-014-0378-1

zbMATH Keywords

algorithmlinear systemscomputer algebra systemsnumerical experimentsymbolic algorithmmatrix decompositioncomputational costperiodic anti-tridiagonal matricesperiodic tridiagonal matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Symbolic computation and algebraic computation (68W30) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (11)

Analytic determinants and inverses of Toeplitz and Hankel tridiagonal matrices with perturbed columns ⋮ The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows ⋮ Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices ⋮ Properties of a class of perturbed Toeplitz periodic tridiagonal matrices ⋮ Anti-diagonalization theory and algorithm of matrices -- from skew-symmetric matrices to arbitrary matrices ⋮ On the efficient and accurate determinant evaluation of periodic tridiagonal Toeplitz matrices ⋮ A structure-preserving algorithm for linear systems with circulant pentadiagonal coefficient matrices ⋮ Numerical algorithm for the determinant evaluation of cyclic pentadiagonal matrices with Toeplitz structure ⋮ A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices ⋮ Explicit determinants, inverses and eigenvalues of four band Toeplitz matrices with perturbed rows ⋮ ON INVERSES AND EIGENPAIRS OF PERIODIC TRIDIAGONAL TOEPLITZ MATRICES WITH PERTURBED CORNERS

Uses Software

• Matlab
• CSparse

Cites Work

• Unnamed Item
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• Direct Methods for Sparse Linear Systems
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• Eigenproblems for Matrices Associated with Periodic Boundary Conditions
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• The solution of periodic tridiagonal linear systems by the stride of 3 reduction algorithm
• Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems
• Perturbation method with triangular propagators and anharmonicities of intermediate strength

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