A fast and reliable numerical solver for general bordered \(k\)-tridiagonal matrix linear equations

DOI10.1016/j.cam.2016.10.004zbMath1357.65033OpenAlexW2538692140MaRDI QIDQ507877

J. Abderramán Marrero, Venancio Tomeo

Publication date: 9 February 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.10.004

zbMATH Keywords

numerical examplesaccuracyinversebordered \(k\)-tridiagonal matrixGivens rotationmatrix linear equationSherman-Morrison's formula

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (5)

An incomplete block-diagonalization approach for evaluating the determinants of bordered \(k\)-tridiagonal matrices ⋮ Numerical algorithms for the determinants of opposite-bordered and singly-bordered tridiagonal matrices ⋮ A reliable Givens-LU approach for solving opposite-bordered tridiagonal linear systems ⋮ Generalized Sherman-Morrison-Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matrices ⋮ On linear-time solvers for comrade linear systems

Uses Software

• mctoolbox
• Mulprec

Cites Work

• Unnamed Item
• A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems
• Some comments on \(k\)-tridiagonal matrices: determinant, spectra, and inversion
• Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
• On the powers and the inverse of a tridiagonal matrix
• On the inverse and determinant of general bordered tridiagonal matrices
• Symbolic algorithms for the inverses of general \(k\)-tridiagonal matrices
• Non-symbolic algorithms for the inversion of tridiagonal matrices
• On new algorithms for inverting Hessenberg matrices
• A note on representations for the inverses of tridiagonal matrices
• Inverses of generalized Hessenberg matrices
• Numerical Methods in Scientific Computing, Volume I
• A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
• Analytical inversion of general tridiagonal matrices
• Accuracy and Stability of Numerical Algorithms

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