A Hessenberg-Schur Method for the Problem AX + XB = C
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ONe of the most effective methods for solving the matrix equation AX + XB = C is the Bartels-Stewart algorithm. Key to this technique is the orthogonal reduction of A and B to triangular form using the QR algorithm for eigenvalues. A new method is proposed which differs from the Bartels-Stewart algorithm in that A is only reduced to Hessenberg form. The resulting algorithm is between 30 and 70 percent faster depending upon the dimensions of the matrices A and B. The stability of the new method is demonstrated through a roundoff error analysis and supported by numerical tests. Fianlly, it is shown how the techniques described can be applied and generalized to other matrix equation problems.
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1978-10
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Cornell University
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computer science; technical report
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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR78-354
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technical report