Palindromic matrix polynomials, matrix functions and integral representations

DOI10.1016/j.laa.2010.09.013zbMath1211.15027OpenAlexW2014871361MaRDI QIDQ609490

Beatrice Meini, Bruno Iannazzo

Publication date: 1 December 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.09.013

zbMATH Keywords

matrix square rootpolar decompositionmatrix functionquadratic matrix equationmatrix geometric meanmatrix signpalindromic matrix polynomial

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Matrices over function rings in one or more variables (15A54)

Related Items (10)

On a class of inverse palindromic eigenvalue problem ⋮ Computing primary solutions of equations involving primary matrix functions ⋮ On the Matrix Square Root via Geometric Optimization ⋮ Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector ⋮ The Padé iterations for the matrix sign function and their reciprocals are optimal ⋮ Fast enclosure for a matrix inverse square root ⋮ The geometric mean of two matrices from a computational viewpoint ⋮ An effective matrix geometric mean satisfying the Ando–Li–Mathias properties ⋮ The palindromic cyclic reduction and related algorithms ⋮ CALCULATION OF THE NUMBER OF PALINDROMS IN A BINARY SYSTEM

Uses Software

• mftoolbox

Cites Work

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• Computing real square roots of a real matrix
• Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms
• Implicit QR algorithms for palindromic and even eigenvalue problems
• Inertia characteristics of self-adjoint matrix polynomials
• The range of \(A^{-1} A^*\) in GL(n,C)
• The matrix sign decomposition and its relation to the polar decomposition
• Geometric means
• The Matrix Square Root from a New Functional Perspective: Theoretical Results and Computational Issues
• The matrix sign function
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Canonical structures for palindromic matrix polynomials
• Functions of Matrices
• Numerical Methods for Structured Markov Chains

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