engleski

Orthosymmetric Block Rotations

Rotations are essential transformations in many parts of numerical linear algebra. In this paper it is shown that there exists a family of matrices unitary with respect to an orthosymmetric scalar product $J$, that can be decomposed into the product of two $J$-unitary matrices---a block diagonal matrix and an orthosymmetric block rotation. This decomposition can be used for computing various one-sided and two-sided matrix transformations by divide-and-conquer or tree-like algorithms. As an illustration, a blocked version of the QR-like factorization of a given matrix is considered.

orthosymmetric unitary matrices; orthosymmetric block rotations; generalized polar decomposition; QR-like factorization; test matrix generation

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