On the determinant evaluation of quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices

DOI10.1007/s10910-013-0224-xzbMath1286.65057OpenAlexW2002871058MaRDI QIDQ2443863

Ji-Teng Jia, Yao-Lin Jiang

Publication date: 8 April 2014

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

Full work available at URL: https://doi.org/10.1007/s10910-013-0224-x

zbMATH Keywords

Toeplitz matrixdeterminanttriangular matrixcomputational costsquasi penta-diagonal matrix

Mathematics Subject Classification ID

Numerical computation of determinants (65F40) Complexity and performance of numerical algorithms (65Y20) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (8)

An efficient numerical algorithm for the determinant of a cyclic pentadiagonal Toeplitz matrix ⋮ Anti-diagonalization theory and algorithm of matrices -- from skew-symmetric matrices to arbitrary matrices ⋮ Numerical algorithms for the determinant evaluation of general Hessenberg matrices ⋮ A symbolic algorithm for periodic tridiagonal systems of equations ⋮ On a homogeneous recurrence relation for the determinants of general pentadiagonal Toeplitz matrices ⋮ On determinants of cyclic pentadiagonal matrices with Toeplitz structure ⋮ Numerical algorithm for the determinant evaluation of cyclic pentadiagonal matrices with Toeplitz structure ⋮ On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices

Uses Software

• Matlab
• CSparse

Cites Work

• Theory and algorithm of the inversion method for pentadiagonal matrices
• An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices
• A computational algorithm for special \(n\)th-order pentadiagonal Toeplitz determinants
• New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems
• Determinants of block tridiagonal matrices
• Symbolic algorithm for inverting cyclic pentadiagonal matrices recursively - derivation and implementation
• A simple adaptive technique for nonlinear wave problems
• The Schur complement and its applications
• On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle
• A novel algorithm for solving quasi penta-diagonal linear systems
• A computational algorithm for solving nearly penta-diagonal linear systems
• A note on computing the inverse and the determinant of a pentadiagonal Toeplitz matrix
• A fast numerical algorithm for the determinant of a pentadiagonal matrix
• Direct Methods for Sparse Linear Systems
• A recursive algorithm for determining the eigenvalues of a quindiagonal matrix
• A fast numerical algorithm for solving nearly penta-diagonal linear systems
• A recursive relation for the determinant of a pentadiagonal matrix
• On Direct Methods for Solving Poisson’s Equations
• Perturbation method with triangular propagators and anharmonicities of intermediate strength

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