dc.contributor.author Higham, Nicholas J. en_US dc.contributor.author Schreiber, Robert S. en_US dc.date.accessioned 2007-04-23T17:34:48Z dc.date.available 2007-04-23T17:34:48Z dc.date.issued 1988-10 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR88-942 en_US dc.identifier.uri https://hdl.handle.net/1813/6782 dc.description.abstract The polar decomposition of an $m x n$ matrix $A$ of full rank, where $m \geq n$, can be computed using a quadratically convergent algorithm of Higham [SIAM J. Sci. Stat. Comput., 7 (1986), pp.1160-1174]. The algorithm is based on a Newton iteration involving a matrix inverse. We show how with the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary $A$. We also describe how to use the algorithm to compute the positive semi-definite square root of a Hermitian positive semi-definite matrix. We formulate a hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bjorck and Bowie. The decision when to switch is made using a condition estimator. This "matrix multiplication rich" algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion. en_US dc.format.extent 889385 bytes dc.format.extent 185559 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject computer science en_US dc.subject technical report en_US dc.title Fast Polar Decomposition of an Arbitrary Matrix en_US dc.type technical report en_US
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