On iterative algorithms for the polar decomposition of a matrix and the matrix sign function
DOI10.1016/j.amc.2015.08.004zbMath1410.15028OpenAlexW1195028917MaRDI QIDQ670807
Paweł Zieliński, Andrzej Kiełbasiński, Krystyna Ziętak
Publication date: 20 March 2019
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2015.08.004
matrix sign functiondual Padé family of iterationsnumerical matrix inversionpolar decomposition of a matrixreciprocal Padé family of iterationsscaled Newton method
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices
- Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix \(p\)th root
- The Padé iterations for the matrix sign function and their reciprocals are optimal
- Algorithms for the matrix sector function
- An optimum iteration for the matrix polar decomposition
- The matrix sign decomposition and its relation to the polar decomposition
- Numerical behaviour of Higham's scaled method for polar decomposition
- The dual Padé families of iterations for the matrix \(p\)th root and the matrix \(p\)-sector function
- The minimization of matrix logarithms: on a fundamental property of the unitary polar factor
- Approximation of matrices and a family of Gander methods for polar decomposition
- Backward Stability of Iterations for Computing the Polar Decomposition
- A Logarithmic Minimization Property of the Unitary Polar Factor in the Spectral and Frobenius Norms
- Optimizing Halley's Iteration for Computing the Matrix Polar Decomposition
- Algorithms for the Polar Decomposition
- Note on “A New Scaling for Newton's Iteration for the Polar Decomposition and Its Backward Stability” by R. Byers and H. Xu
- A New Scaling for Newton's Iteration for the Polar Decomposition and its Backward Stability
- A Family of Rational Iterations and Its Application to the Computation of the Matrix pth Root
- Matrix sector functions and their applications to systems theory
- Computing the Polar Decomposition—with Applications
- The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators
- Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
- Stability of Methods for Matrix Inversion
- On Scaling Newton’s Method for Polar Decomposition and the Matrix Sign Function
- On K nig's root-finding algorithms*
- A Padé family of iterations for the matrix sign function and related problems
- Rational Iterative Methods for the Matrix Sign Function
- Functions Preserving Matrix Groups and Iterations for the Matrix Square Root
- Functions of Matrices
- An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix
This page was built for publication: On iterative algorithms for the polar decomposition of a matrix and the matrix sign function