The Parameterized Sr Algorithm for Symplectic (butterfly) Matrices
نویسنده
چکیده
The SR algorithm is a structure-preserving algorithm for computing the spectrum of symplectic matrices. Any symplectic matrix can be reduced to symplectic butterfly form. A symplectic matrix B in butterfly form is uniquely determined by 4n− 1 parameters. Using these 4n− 1 parameters, we show how one step of the symplectic SR algorithm for B can be carried out in O(n) arithmetic operations compared to O(n3) arithmetic operations when working on the actual symplectic matrix. Moreover, the symplectic structure, which will be destroyed in the numerical process due to roundoff errors when working with a symplectic (butterfly) matrix, will be forced by working just with the parameters.
منابع مشابه
The parameterized SR algorithm for symplectic (butterfly) matrices
The SR algorithm is a structure-preserving algorithm for computing the spectrum of symplectic matrices. Any symplectic matrix can be reduced to symplectic butterfly form. A symplectic matrix B in butterfly form is uniquely determined by 4n− 1 parameters. Using these 4n− 1 parameters, we show how one step of the symplectic SR algorithm for B can be carried out in O(n) arithmetic operations compa...
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تاریخ انتشار 2001