Fast block diagonalization of \(k\)-tridiagonal matrices

DOI10.1016/j.amc.2011.08.014zbMath1478.65015OpenAlexW2025685930MaRDI QIDQ425465

Tomohiro Sogabe, Moawwad E. A. El-Mikkawy

Publication date: 8 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.08.014

zbMATH Keywords

finite fielddeterminantgeneral linear group\(k\)-tridiagonal matrixblock diagonalizationsgeneralized \(k\)-Fibonacci numbers

Mathematics Subject Classification ID

Numerical computation of determinants (65F40) Direct numerical methods for linear systems and matrix inversion (65F05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

A block diagonalization based algorithm for the determinants of block \(k\)-tridiagonal matrices, A note on a fast breakdown-free algorithm for computing the determinants and the permanents of \(k\)-tridiagonal matrices, An incomplete block-diagonalization approach for evaluating the determinants of bordered \(k\)-tridiagonal matrices, On decomposition of \(k\)-tridiagonal \(\ell\)-Toeplitz matrices and its applications, A bidiagonalization-based numerical algorithm for computing the inverses of \((p, q)\)-tridiagonal matrices, A tridiagonalization-based numerical algorithm for computing the inverses of \((p, q)\)-pentadiagonal matrices, Explicit formula for positive integer powers of \(k\)-tridiagonal Toeplitz matrices, Some comments on \(k\)-tridiagonal matrices: determinant, spectra, and inversion, Elliptical higher rank numerical range of some Toeplitz matrices, Symbolic algorithms for the inverses of general \(k\)-tridiagonal matrices, Eigenvalue clustering of coefficient matrices in the iterative stride reductions for linear systems, On singular values related to DAEs in Kronecker canonical form, Bidiagonalization of \((k, k + 1)\)-tridiagonal matrices, A new recursive algorithm for inverting general \(k\)-tridiagonal matrices, A novel algorithm for inverting a general \(k\)-tridiagonal matrix, A periodic determinantal property for (0,1) double banded matrices

Uses Software

• JDQR
• JDQZ
• CSparse

Cites Work

• A new family of \(k\)-Fibonacci numbers
• A fast algorithm for evaluating \(n\)th order tri-diagonal determinants.
• On a constant-diagonals matrix
• On computing the determinants and inverses of some special type of tridiagonal and constant-diagonals matrices
• THE LU FACTORIZATIONS AND DETERMINANTS OF THE K-TRIDIAGONAL MATRICES
• Direct Methods for Sparse Linear Systems
• Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix
• Templates for the Solution of Algebraic Eigenvalue Problems
• The inverse of a tridiagonal matrix