Computing the polar decomposition with applications
SIAM Journal on Scientific and Statistical Computing
Algorithms for the polar decomposition
SIAM Journal on Scientific and Statistical Computing
On scaling Newton's method for polar decomposition and the matrix sign function
SIAM Journal on Matrix Analysis and Applications
A parallel algorithm for computing the polar decomposition
Parallel Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Large-scale electronic structure calculations of high-Z metals on the BlueGene/L platform
Proceedings of the 2006 ACM/IEEE conference on Supercomputing
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Architecture of Qbox: a scalable first-principles molecular dynamics code
IBM Journal of Research and Development
A New Scaling for Newton's Iteration for the Polar Decomposition and its Backward Stability
SIAM Journal on Matrix Analysis and Applications
Dynamic task scheduling for linear algebra algorithms on distributed-memory multicore systems
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
SIAM Journal on Matrix Analysis and Applications
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We introduce a dynamically weighted Halley (DWH) iteration for computing the polar decomposition of a matrix, and we prove that the new method is globally and asymptotically cubically convergent. For matrices with condition number no greater than $10^{16}$, the DWH method needs at most six iterations for convergence with the tolerance $10^{-16}$. The Halley iteration can be implemented via QR decompositions without explicit matrix inversions. Therefore, it is an inverse free communication friendly algorithm for the emerging multicore and hybrid high performance computing systems.