An incomplete block-diagonalization approach for evaluating the determinants of bordered \(k\)-tridiagonal matrices

DOI10.1007/s10910-022-01377-0zbMath1505.65176OpenAlexW4285092207WikidataQ114225642 ScholiaQ114225642MaRDI QIDQ2160361

Kai-Kai Zhang, Bao-Ming Zhong, Ji-Teng Jia, Jie Wang, Ting-Feng Yuan

Publication date: 3 August 2022

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

Full work available at URL: https://doi.org/10.1007/s10910-022-01377-0

zbMATH Keywords

determinantsbreakdown-free algorithm\(k\)-tridiagonal matricesbordered tridiagonal matricesblock-diagonalizations

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Determinants, permanents, traces, other special matrix functions (15A15) Numerical computation of determinants (65F40) Linear transformations, semilinear transformations (15A04)

Related Items (1)

On the efficient and accurate determinant evaluation of periodic tridiagonal Toeplitz matrices

Uses Software

• Matlab

Cites Work

• A note on a fast breakdown-free algorithm for computing the determinants and the permanents of \(k\)-tridiagonal matrices
• Fast block diagonalization of \(k\)-tridiagonal matrices
• A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems
• A fast and reliable numerical solver for general bordered \(k\)-tridiagonal matrix linear equations
• A block diagonalization based algorithm for the determinants of block \(k\)-tridiagonal matrices
• High order accurate, one-sided finite-difference approximations to concentration gradients at the boundaries, for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry.
• A specialised cyclic reduction algorithm for linear algebraic equation systems with quasi-tridiagonal matrices
• Numerical algorithms for the determinants of opposite-bordered and singly-bordered tridiagonal matrices
• A fast elementary algorithm for computing the determinant of Toeplitz matrices
• A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices
• A scheme for imposing constraints and improving conditioning of structural stiffness matrices
• Mathematical Modeling of Biosensors
• High-order spatial discretisations in electrochemical digital simulation. 1. Combination with the BDF algorithm

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