Approximating the matrix sign function using a novel iterative method

DOI10.1155/2014/105301zbMath1470.65082OpenAlexW2081090833WikidataQ59035239 ScholiaQ59035239MaRDI QIDQ1722105

Xianqiang Yang

Publication date: 14 February 2019

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/105301

Mathematics Subject Classification ID

Numerical linear algebra (65F99) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (11)

Construction of a convergent scheme for finding matrix sign function ⋮ A generalized Steffensen's method for matrix sign function ⋮ A globally convergent variant of mid-point method for finding the matrix sign ⋮ Constructing a high-order globally convergent iterative method for calculating the matrix sign function ⋮ A novel iterative method for polar decomposition and matrix sign function ⋮ An algorithm for computing geometric mean of two Hermitian positive definite matrices via matrix sign ⋮ Numerically stable improved Chebyshev-Halley type schemes for matrix sign function ⋮ Several numerical methods for computing unitary polar factor of a matrix ⋮ Efficient iterative methods with and without memory possessing high efficiency indices ⋮ New iterative methods for finding matrix sign function: derivation and application ⋮ A fourth-order method for computing the sign function of a matrix with application in the Yang-Baxter-like matrix equation

Uses Software

• mftoolbox

Cites Work

• A note on mode decoupling of linear time-invariant systems using the generalized sign matrix
• Algorithms for the matrix sector function
• Solving stable generalized Lyapunov equations with the matrix sign function
• The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces
• The sign matrix and the separation of matrix eigenvalues
• Some matrix iterations for computing matrix sign function
• Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function
• Matrix-sign algorithms for Riccati equations
• A Family of Rational Iterations and Its Application to the Computation of the Matrix pth Root
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• The Matrix Sign Function Method and the Computation of Invariant Subspaces
• Using the Matrix Sign Function to Compute Invariant Subspaces
• The matrix sign function
• Rational Iterative Methods for the Matrix Sign Function
• Functions of Matrices
• Some Fourth Order Multipoint Iterative Methods for Solving Equations
• The Mathematica GuideBook for Numerics

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