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• W2000580198 abstract "The Wedderburn rank reduction formula is a powerful method for developing matrix factorizations and many fundamental numerical linear algebra processes. We present a new interpretation of the Wedderburn rank reduction formula and its associated biconjugation process and see a more extensive result of the formula. In doing this, we propose a new formulation based on the null space transformations on rows and columns of A simultaneously, and show several matrix factorizations that can be derived from the Wedderburn rank reduction formula. We also present a generalization of the biconjugation process and compute banded and Hessenberg factorizations. Using the new formulation, we compute the WZ and ZW factorizations of a nonsingular matrix as well as the and the factorizations of a symmetric positive definite matrix. Then, we develop the integer Wedderburn rank reduction formula and its integer biconjugation process and present a class of algorithms for computing all integer matrix factorizations such as the integer LU factorization and the Smith normal form of an arbitrary integer matrix." @default.
• W2000580198 created "2016-06-24" @default.
• W2000580198 creator A5062019109 @default.
• W2000580198 creator A5089564110 @default.
• W2000580198 date "2015-02-11" @default.
• W2000580198 modified "2023-10-17" @default.
• W2000580198 title "Real and integer Wedderburn rank reduction formulas for matrix decompositions" @default.
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• W2000580198 doi "https://doi.org/10.1080/10556788.2014.1002192" @default.
• W2000580198 hasPublicationYear "2015" @default.
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