Simultaneous triangularization of commuting matrices for the solution of polynomial equations

DOI10.2478/s11533-011-0106-zzbMath1245.65041OpenAlexW1978470432MaRDI QIDQ432249

Vanesa Cortés, Thomas Sauer, Juan Manuel Peña

Publication date: 3 July 2012

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-011-0106-z

zbMATH Keywords

numerical examplespolynomial systemcommuting matricessimultaneous triangularizationjoint eigenvaluesQR-method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of solutions to systems of equations (65H10) Numerical computation of roots of polynomial equations (65H04)

Cites Work

• On the accuracy of the Gerschgorin circle theorem for bounding the spread of a real symmetric matrix
• On an alternative to Gerschgorin circles and ovals of Cassini
• Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
• H-bases for polynomial interpolation and system solving
• A Class of P-Matrices with Applications to the Localization of the Eigenvalues of a Real Matrix
• Polynomial Interpolation in Several Variables: Lattices, Differences, and Ideals
• Numerical Methods for Simultaneous Diagonalization
• Symbolic solution of large stationary chemical kinetics problems
• A Chart of Numerical Methods for Structured Eigenvalue Problems
• Matrix eigenproblems are at the heart of polynomial system solving
• Multivariate polynomial system solving using intersections of eigenspaces.
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